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Lingaya’s University( U / S 3 o f U G C A c t , 1 9 5 6 )

Department of Mechanical Engineering

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Workbook on

DYNAMICS (TOM-I)

Department of Mechanical Engineering

LINGAYA’S UNIVERSITY(Deemed to be University under Section 3 of UGC Act, 1956)

Nachauli, Old Faridabad – Jasana RoadFaridabad 121 002, Haryana, India

DynamicsChapter Title Page

I. Kinematics of a Particle 1-10

Rectilinear KinematicsGraphical SolutionsCurvilinear motion:Rectangular CoordCurvilinear motion: Normal & Tangential CoordCurvilinear motion: Cylindrical CoordDependant and relative motion analysis

II Kinetics of a Particle: Force and Acceleration 11-15

Equations of Motion: Rectangular Coord Eqn's of Motion: Normal & Tangential Coord Equations of Motion: Cylindrical Coord

III Kinetics of a Particle: Work and Energy 16-21

Principle of Work & Energy Power and Efficiency Conservation of Energy Theorem

IV Kinetics of a Particle: Impulse and Momentum 22-29Principle of Linear Impulse and Momentum Conservation of Linear Momentum Impact Principle of Angular Impulse and Momentum

V Planar Kinematics of a Rigid Body 30-37Rotation About a Fixed Axis Absolute General Plane Motion Analysis Relative Motion Analysis: Velocity Instantaneous Centre of Zero Velocity Relative Motion Analysis: Acceleration

VI Planar Kinetics of a Rigid Body: Force and Acceleration 38-41

Mass Moment of Inertia Equations of Motion: Translation Equations of Motion: Rotation about a Fixed Axis Equations of Motion: General Plane Motion

VII Planar Kinetics of a Rigid Body: Work and Energy 42-47

Principle of Work and Energy Conservation of Energy

VIII Planar Kinetics of a Rigid Body:Impulse and Momentum 48-49

Principle of Impulse and Momentum

IX Keywords 50-53

http://www.lboro.ac.uk/faculty/eng/engtlsc/Eng_Mech/tutorials/tut19_1_2.htm

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Kinematics of Particle:

Rectilinear Kinematics

1) If a = (2t) m/s2, where t is in seconds, calculate the particle's velocity when t = 2s. When t = 0, Vo = 2m/s.

v = ? One answer only.

0 m/s

2 m/s

4 m/s

6 m/s

none of the above

2) If s = (4t2) m, calculate the particle's acceleration at t = 2s.

a = ? One answer only.

2 m/s2

4 m/s2

8 m/s2

16 m/s2

none of the above

3) If s = (3t2) m, where t is in secs, calculate the particle velocities when t = 1s.


0 m/s

3 m/s

4 m/s

6 m/s

none of the above

4) The particle shown in the figure travels from A to B in 1s, it then travels from B to C in 1s. Calculate the average speed during the entire time period.

Chapter I


1 m/s

3 m/s

5 m/s

-2 m/s

none of the above

5) cont....What is the average velocity?


1 m/s

2 m/s

-1 m/s

-5 m/s

none of the above

6) When t = 0 a particle is located at s = 3m and has a velocity of v = 2 m/s. If its acceleration is a = 2m/s2, determine its position when t = 1s.

s = ? One answer only.

3 m

5 m

6 m

8 m

none of the above

7) A ball is tossed downward from A with an initial speed of VA = 2m/s. If it takes 1 second to strikethe ground, determine height h.

h = ? One answer only.

2.9 m

4.9 m

6.9 m

9.81 m

none of the above

Graphical Solution

1) Given the s - t graph. Calculate the particle's velocity when t=1s.


0.5 m/s

1 m/s

2 m/s

none of the above

2) Given the a - s graph. If v = 0 at s = 0, calculate the particle's speed when s = 5m.


2.5 m/s

4 m/s

5 m/s

10 m/s

12.5 m/s

none of the above

3) Given the v - s graph. Calculate the particle's acceleration when s = 2m.


9 m/s2

18 m/s2

27 m/s2

none of the above

4) Given the v - t graph. Calculate the particle's acceleration when t = 3s.


-1.67 m/s2

-5 m/s2

-10 m/s2

-15 m/s2

none of the above

5) cont....Calculate the particle's position when t = 1s. When t = 0, s = 1m.


10 m

11 m

15 m

none of the above

6) Given the v - t graph. If s = 1m when t = 0, calculate the particle's position at t = 4s


0 m

1 m

16 m

17 m

none of the above

7) Given the a - t graph. If v = 6m/s when t = 0, calculate the time t needed to stop the particle.

t = ? One answer only.

6 s

9 s

12 s

15 s

none of the above

Curvilinear Motion: Rectangular Coord

1) If v = (8ti + 9t2j) m/s, where t is in seconds, determine the distance from the origin to the particle when t = 1s.


4 m

5 m

3 m

none of the above

2) When t = 0 a particle is at the origin. If its x component of velocity is constant, v = 4m/s, calculatethe distance it travels along the x axis in t = 2s.

x = ? One answer only.

8 m

8.5 m

10 m

none of the above

3) cont....If its y component of acceleration is ay = 3m/s2, calculate how far it travels along the y axis in t = 2s. When t = 0, vy = 0.

y = ? One answer only.

2 m

5 m

6 m

none of the above

4) cont....How far is the particle from the origin in t = 2s?

d = ? One answer only.

9 m

10 m

12 m

none of the above

5) A particle travels from A to B in four seconds then from B to C in six seconds. What is the particle's average velocity?

vavg = ? One answer only.

(-4i - 3j) m/s

(-0.4i - 0.3j) m/s

(0.4i + 0.3j) m/s

(-0.4i + 0.3j) m/s

none of the above

6) cont....What is the particle's average speed?

vsp = ? One answer only.

2 m/s

1.5 m/s

0.7 m/s

0.5 m/s

none of the above

7) A ball is thrown horizontally from A with a speed of vA = 6m/s as shown. If it strikes the ground in t = 1s determine the height h.


4.905 m

9.81 m

10.9 m

16.1 m

none of the above

8) cont....Calculate the range R.

R = ? One answer only.

3 m

4 m

6 m

12 m

none of the above

9) A ball is thrown at an angle of 45o from the horizontal with a speed of vA = 9.81(2)0.5 m/s. Determine the maximum height h it attains.


9.81 m

4.905 m

14.72 m

19.62 m

none of the above

10) cont....How much time does it take to travel from A to C?


1 s

4 s

3 s

2 s

none of the above

11) cont....What is the range R?

R = ? One answer only.

9.81 m

14.71 m

19.62 m

39.24 m

none of the above

12) A ball is launched as shown. Select the equation that describes its position y as a function of time.

One answer only.

y = 10sin45t - (0.5)(9.81)t2

y = 10sin45t - (2)(9.81)t

y = 10sin45t + (0.5)(9.81)t2

y = 10sin45t - (9.81)t2

none of the above

Curvilinear Motion: Normal and Tang.Coord

1) A particle P is traveling around a circular path such that at the instant considered, the speed is 3m/s and increasing at 4m/s2. Calculate the magnitude of the particle's acceleration at this instant.


0 m/s2

3 m/s2

4 m/s2

5 m/s2

none of the above

2) When t = 0, s = 0.5, v = 1m/s. If v = (3t + 1) m/s, where t is in seconds, compute the distance s traveled by the particle when t = 1s.


3 m

3.5 m

4.5 m

6 m

none of the above

3) cont....What is the speed of the particle when t = 1s.


3 m/s

4 m/s

5 m/s

6 m/s

none of the above

4) cont....What is the acceleration of the particle when t = 1s?


2 m/s2

3 m/s2

4 m/s2

5 m/s2

none of the above

5) When s = 0, v = 0. If at = (4s) m/s2, where s is in meters, calculate the particle's speed when s = 1m.


2 m/s

4 m/s

5 m/s

none of the above

6) cont...What is the magnitude of acceleration when s = 1m?


2 m/s2

3 m/s2

4 m/s2

5 m/s2

none of the above

7) A particle is traveling along a parabolic path with a constant speed of 2m/s. Determine the radius of curvature ρ (roa) at A.

ρ = ? One answer only.

0.5 m

1 m

1.5 m

2 m

none of the above

8) cont....What is the particle's acceleration at A.


1 m/s2

2 m/s2

4 m/s2

8 m/s2

none of the above

Curviliner Motion: Cylindrical Coord

1) A particle moves along a path such that its position as a function of time is defined by the equation r = (6t) m, θ = (t2) rad, where t is in secs. Calculate ar at t = 1s.

ar = ? One answer only.

24 m/s2

-30 m/s2

-24 m/s2

-18 m/s2

none of the above

2) cont....Now calculate aθ.

aθ = ? One answer only.

36 m/s2

12 m/s2

24 m/s2

-12 m/s2

none of the above

3) A particle P is moving along the path with a speed of 10m/s at the instant r = 6m. If the radial coordinate is increasing at the rate of = 8m/s, calculate the rate of increase of , measured in rad/s.

= ? One answer only.

0.33 rad/s

1 rad/s

1.67 rad/s

2 rad/s

none of the above

4) A particle moves along a circular path defined by r = (2cosθ) m. If the rate of increase of θ is always constant, such that = 2 rad/s, compute vr when θ = 0o.

vr = ? One answer only.

4 m/s

0 m/s

2 m/s

-4 m/s

none of the above

5) cont....What is vθ at θ = 0o?

vθ = ? One answer only.

4 m/s

-4 m/s

2 m/s

-2 m/s

none of the above

6) A particle moves along a spiral path r = (4θ) m, where θ is in radians, such that it maintains a constant speed of v = 4(2)0.5 m/s. Calculate at the instant θ = 1 rad.

= ? One answer only.

0 rad/s

4 rad/s

2 rad/s

1 rad/s

none of the above

Dependent and Relative Motion Analysis

1) Select the equation which relates the position of the end of the cable B to the position of block A.

One answer only.

SB + 2SA = L

SB+ 3SA = L

SB + SA = L

2SB + SA = L

none of the above


One answer only.

3SA + SB = L

4SA + SB = L

SA + 2SB = L

2SA + SB = L

none of the above


One answer only.

3SB + SA= L

SB + 3SA = L

3SB + 2SA = L

2SB + 3SA = L

none of the above

4) End A of the cord is moving 6m/s to the left. Compute the velocity of the block B.

vB = ? One answer only.

2 m/s (to left)

3 m/s (to left)

6 m/s (to left)

12 m/s (to left)

none of the above

5) At a given instant blocks A and B have the motion shown. Compute the velocity of the block B with respect to block A.

vB/A = ? One answer only.

6i m/s

-6i m/s

-2i m/s

2i m/s

none of the above

6) At a given instant blocks A and B have the motion shown. Compute the acceleration of block B with respect to block A.

aB/A = ? One answer only.

2i m/s2

1i m/s2

-1i m/s2

0 m/s2

none of the above

Equations of Motion: Rectangular Coord

1) An inertial coordinate system can rotate with constant angular velocity.

One answer only.

True

False

2) A 10 Kg block rests on a smooth surface. On a sheet of paper draw the block's free-body diagram, establish the x,y coordinate system, and compute the block's initial acceleration.


0 m/s2

2 m/s2

5 m/s2

10 m/s2

None of the above



0 m/s2

9.81 m/s2

10 m/s2

19.81 m/s2

None of the above

Chapter II



0 m/s2

5 m/s2

15 m/s2

20 m/s2

None of the above

5) Calculate the acceleration of the 10 kg block A. Neglect the mass of the pulley.


0 m/s2

4.905 m/s2

9.81 m/s2

19.62 m/s2

None of the above

6) cont.... If a 20 Kg block (weight = 196.2N) was suspended from B to replace the 196.2 N force, what would the acceleration of block A be?

One answer only.

Greater than 9.81 m/s2

Less than 9.81 m/s2

Equal to 9.81 m/s2

7) The 10 Kg block rests on a smooth surface and is acted upon by the force shown. Calculate its velocity when t = 1s. The block is initially at rest.


9.81 m/s

10 m/s

19.62 m/s

None of the above

8) The collar has a mass of 10 Kg, and the coefficient of kinetic friction between the collar and rod is µk = 0.3. Select the equation of motion for the collar in the x direction from the list.

One answer only.

98.1cos30 + 0.3Nc = 10a

98.1sin30 - 0.3Nc = 10a

98.1sin30 + 0.3Nc = -10a

98.1cos30 - 0.3Nc = 10a

None of the above

Equations of Motion: Normal & Tang.Coord

1) The block has a mass of 0.4 Kg and is subjected to a uniform circular motion about the vertical axis. If the tensile strength of the cord AB is 200N, calculate the constant speed of the block that will break the cord. Neglect friction.


5 m/s

10 m/s

25 m/s

50 m/s

None of the above

2) The block has a mass of 2 Kg and is held up against the wall of the rotating surface by centrifugal force. If the coefficient of static friction between the block and the wall is µs = 0.3, select the equation of the motion for the block in the b direction.

One answer only.

0.3NB - 19.62 = 0

0.3NB - 19.62 = 2ab

0.3NB - 19.62 = -2ab

0.3NB + 19.62 = 2ab

None of the above

3) The 10 Kg block is resting on the rotation platform. At the instant shown the block's tangential speed is 2 m/s, and the speed is increasing at 1 m/s2. If the surface of the platform is rough, calculate the magnitude of the frictional force acting on the block in the t direction.

Ft = ? One answer only.

30 N

40 N

68.1 N

98.1 N

None of the above

4) The 10 Kg block is travelling along the smooth path. Calculate its greatest speed at A so it does not leave the path. The radius of curvature at this point is ρ= 2 m.


19.62 m/s

(9.81)1/2 m/s

(19.62)1/2 m/s

2(9.81)1/2 m/s

None of the above

5) The 10 Kg block is released from rest at A and slides down along the smooth curved path. Select the equation of motion for the block in the t direction.

One answer only.

98.1sinθ = 10at

-98.1sinθ = 10at

98.1cosθ = 10at

-98.1cosθ = 10at

None of the above

6) Cont....Select the equation of motion for the block in the n direction.

One answer only.

NB - 98.1sinθ = 5v2

NB - 98.1cosθ = 10v2

98.1cosθ - NB = 5v2

NB + 98.1sinθ = 5v2

None of the above

Equations of Motion: Cylindrical Coord

1) The planar motion of a 0.5 Kg particle is defined by the equations r = (6t2) m and θ = t rad, where t is in seconds. Determine the magnitude of the radial component of force acting on the particle when t = 1 s.

Fr = ? One answer only.

1.5 N

3 N

6 N

9 N

None of the above

2) cont.... What is the transverse component of force acting on the particle?

Fθ = ? One answer only.

9 N

12 N

15 N

24 N

None of the above

3) The 3 Kg particle P is moving along the horizontal circular path at a constant angular rate of = 2 rad/s. Compute the magnitude of the radial force on the particle.

Fr = ? One answer only.

6 N

0 N

-3 N

-6 N

None of the above

4) Use the equation tan(psi) = r/(dr/dθ) and determine the angle psi made between the extended radial line at θ = 1 rad and the tangent to the curve r = (1θ) m, where θ is in radians.

θ = ? One answer only.

30o

45o

60o

90o

None of the above

5) The equation for the circle is r = 4cosθ m. Use the equation tan (psi) = r/(dr/dθ) and calculate theangle psi made between the extended radial line at θ = 45o and the tangent to the curve. Show the result on a sketch of the curve.

Psi = ? One answer only.

45o

-45o

30o

-30o

None of the above

Kinetics of a Particle: Work & Energy .

Principal of W&E

1) Determine the work done by the force when it is subjected to the displacement indicated.

Chapter III

U = ? One answer only.

0 J

2 J

10 J

20 J

None of the above



0 J

2 J

10 J

20 J

None of the above



2 J

10 J

20 J

None of the above



5 J

5π J

10 J

10π J

None of the above

5) Determine the work done by the force on the spring when it is subjected to the displacement indicated.


-50 J

25 J

50 J

100 J

None of the above

6) Determine the Kinetic energy of the 2 Kg block when it is at point A.

T = ? One answer only.

0 J

2 J

4 J

8 J

None of the above

7) cont....What is the kinetic energy of the block when it is at point B if it still has a speed of 2 m/s?

T = ? One answer only.

0 J

2 J

4 J

8 J

None of the above

8) A 2 Kg block is moving to the right at 10 m/s when it is acted upon by the 10N force. If the surface is smooth, calculate the distance d the block moves before it stops and the time it takes to stop.

d = ? One answer only.

0 m

5 m

10 m

None of the above

9) cont...From qu 8, time taken for block to come to rest = ? secs

One answer only.

1 s

2 s

4 s

5 s

None of the above

10) The 5 Kg block compresses the spring 2 m. If it is released from rest, determine the block's speed at the instant the spring becomes unstretched. The surface is smooth.


4 m/s

5 m/s

16 m/s

20 m/s

None of the above

11) The 10 Kg ball is released from rest at A. Select from the list the reduced form of the equation of work and energy, necessary to determine the ball's speed when it reaches point B. The cord strikes the fixed peg at C.

One answer only.

196.2 = 5vB2

98.1 = 5 vB2

49.05 = 10 vB2

98.1 = 10 vB2

None of the above

Power & Efficiency

1) Calculate the power developed by the 100 N force which acts on the 10 Kg block. The block has aspeed of 2 m/s.

P = ? One answer only.

0 W

50 W

100 W

200 W

None of the above

2) Calculate the power developed by the 100 N force which acts on the 10 Kg block. The block has aspeed of 2 m/s.


50 W

100 W

200 W

250 W

None of the above

3) Calculate the power developed by the 100 N force after the 10 Kg block has been displaced a distance s as indicated. The block is originally at rest on a smooth surface.


100 W

500 W

1000 W

1200 W

None of the above

4) Calculate the power developed by the 100 N force after the 10 Kg block has been displaced a distance s as indicated. The block is originally at rest on a smooth surface.


20 W

50 W

150 W

None of the above

5) Calculate the power developed by the 100 N force after the 10 Kg block has been displaced a distance s as indicated. The block is originally at rest on a smooth surface. When s = 0 the spring is unstretched.


160 W

240 W

400 W

500 W

None of the above

6) A motor pulls the 10 Kg block forward with a constant velocity of v = 9 m/s. If the coefficient of kinetic friction between the block and the surface is µk = 0.1, and the motor has an efficiency of e = 0.9, determine the required power which must be supplied by the motor.


79.5 W

88.3 W

98.1 W

100 W

None of the above

7) cont....Solve the problem if at the instant considered the block has a velocity of 9 m/s and an acceleration of 1 m/s2


98.1 W

178.3 W

198.1 W

220.1 W

None of the above

Conservation of Energy Theorem

1) Compute the potential energy of the 10 Kg block with respect to the datum.

V = ? One answer only.

98.1 J

-98.1 J

196.2 J

-196.2 J

None of the above

2) Compute the potential energy of the 10 Kg block with respect to the datum.

V = ? One answer only.

40 J

80 J

20 J

-80 J

None of the above

3) The 10 Kg block is released from rest at A. Select the equation that represents the reduced form of the conservation of energy theorem, necessary to determine the maximum compression h in the spring at B. Place the datum at A.

One answer only.

0 = -98.1h - 98.1 - 50h2

0 = -98.1h + 50h2

0 = -98.1 - 98.1h + 50h2

0 = -98.1 - 50h2

None of the above

4) The 10 Kg block is moving freely down the smooth curved path with a speed of 2 m/s when it is at A. Select the equation which represents the reduced form of the conservation of energy theorem, necessary to determine the block's speed at B. Place the datum at A.

One answer only.

20 = 5vB2 - 98.1(3 - 3cos45)

-20 = 5vB2 + 98.1(3 + 3cos45)

20 = 5vB2 + 98.1(3 - 3cos45)

20 = -5vB2 - 98.1(3 - 3cos45)

None of the above

5) The collar has a mass of 10 Kg and slides along the smooth rod. When it is at A it has a downward velocity of 2 m/s. If the spring has an unstretched length of 1 m, select the equation which represents the reduced form of the conservation of energy theorem, necessary to determine the collar's speed when it is at B. Place the datum at A.

One answer only.

1580 = 5vB2 + 10(9.81)(4) - 400

1620 = 5vB2 + 10(9.81)(4) + 400

1620 = 5vB2 - 10(9.81)(4) + 400

1620 = 5vB2 - 10(9.81)(4) - 400

None of the above

6) The spring is compressed 0.2 m and released when the 2 Kg bob is resting on it at A. Select the equation that represents the reduced form of the conservation of energy theorem, necessary to determine the bob's speed when it reaches B. Place the datum at A.

One answer only.

40 = vB2 - 3(9.81)

40 = vB2 +4.5(9.81)

40 = vB2 + 3(9.81)

40 = vB2

None of the above

Principle of Linear Impulse and Momentum

Chapter IV

1) The force F acts for 2 s. Compute the magnitude of the impulse given to the 10-kg block.

I = ? One answer only.

20 Ns

35 Ns

40 Ns

None of the above

2) The force F acts for 2 s. Compute the magnitude of the impulse given to the 10-kg block.

I = ? One answer only.

5 Ns

15 Ns

20 Ns

None of the above

3) Compute the magnitude of the block's linear momentum when the block is at point A. The block has a mass of 10 kg and moves along the vertical curved path with a constant speed of 2 m/s.

LA = ? One answer only.

17 kg.m/s

20 kg.m/s

25 kg.m/s

None of the above

4) cont....What is the magnitude of the linear momentum of the block when it is at point B?

LB = ? One answer only.

5

15

25

None of the above

5) The 2 kg block is moving to the right at 10 m/s when it is acted upon by the 10-N force. If the surface is smooth, determine the time needed to stop the block.


2 s

3.5 s

4.5 s

None of the above

6) The 10 kg block is sliding down the plane at 2 m/s when it is at A. Select the equation which represents a reduced form of the principle of impulse and momentum in the x direction for the time period t = 2 s. The coefficient of kinetic friction between the block and plane is µ = 0.4.

One answer only.

20 - 0.8 NA = 10 v

118.1 - 0.8 NA = 10 v

None of the above

7) The 10 kg ball rolls to the left at 3 m/s, it strikes the wall and bounds back and rolls to the right at 2 m/s. If the contact time is 0.1 s, determine the average impulsive force which the wall exerts on the ball.

F = ? One answer only.

100 N

200 N

300 N

500 N

None of the above

8) The 10 kg block is moving to the right at 3 m/s when it is acted upon by the force F which varies as shown. Select the equation that represents a reduced form of the principle of impulse and momentum in the x direction during the time period t = 5 s. The coefficient of kinetic friction between the block and the plane is µK = 0.4.

One answer only.

90 - 2 NA = 10v

110 - 2 NA = 10v

10 + 2 NA = 10v

None of the above

Conservation of Linear Momentum

1) Blocks A and B have a mass of 10 kg and 20 kg, respectively. If they are travelling with the speeds shown, determine their common velocity if they collide and become coupled together.


2 m/s to right

2 m/s to left

3.33 m/s to left

4 m/s to left

None of the above

2) A spring is placed between the 10-kg block A and the 20-kg block B. The blocks are then pushed together so as to compress the spring and then released from rest. When they "fly" apart it is observed that B travels at 3 m/s to the right. Determine the velocity of block A. The spring is not connected to the blocks and its mass can be neglected. Neglect friction.

vA = ? One answer only.

6 m/s to right

6 m/s to left

12 m/s to left

None of the above

3) cont....Determine the average spring force which acts between each block if the spring remains in contact with the blocks 0.1 s after they are released.


600 N

675 N

725 N

None of the above

4) Indicate the forces that can be neglected ("nonimpulsive") when applying an impulse-momentum analysis to block A just before to just after collision.

Choose 2 of the following options.

Normal force of floor on A

Weight of A

Weight of B

5) Indicate the forces that can be neglected ("nonimpulsive") when applying an impulse-momentum analysis to block A just before to just after collision.

One answer only.

Weight of A

Normal force of wall on A

None of the above

6) The toboggan has a mass of 50 kg and riders A and B each have a mass of 50 kg. Select the equation that represents the solution for the speed of the toboggan when it reaches point D.

One answer only.

98.1(150) = 75(vD)12

98.1(50) = 75(vD)12

None of the above

7) cont....If one rider pushes the other off at D, select the equation for finding the final velocity of the toboggan.

One answer only.

(vD)22 = 3(14)

(vD)22 = 1.5(14)

None of the above

Impact

1) Compute the coefficient of restitution e between the balls, knowing their velocities just before and just after collision.

e = ? One answer only.

0.8

0.5

0.4

None of the above

2) Compute the coefficient of restitution e between the balls, knowing their velocities just before and just after collision.

e = ? One answer only.

0.2

0.4

0.8

None of the above

3) Blocks A and B have a mass of 10 kg and 20 kg, respectively. If they are moving as shown before collision, select the reduced form of the conservation of momentum equation for the blocks. Assume that after collision both blocks move to the right.

One answer only.

6 = (vA)2 + 2(vB)2

10 = (vA)2 + 2(vB)2

None of the above

4) cont....If e = 0.6, select the reduced form of the coefficient of restitution equation for the blocks.

One answer only.

4.2 = (vB)2 - (vA)2

5.4 = (vB)2 - (vA)2

None of the above

5) The 10-kg ball rolls toward the wall with a speed of 5 m/s. If the coefficient of restitution is e = 0.2, determine the speed at which the ball rebounds away from the wall.

v2 = ? One answer only.

0 m/s

3 m/s

1 m/s

None of the above

6) cont....If the ball contacts the wall for t = 0.1 s, determine the net force of the wall on the ball.


400 N

600 N

750 N

None of the above

7) The bob has a mass mA and is released from rest when θ = 90o. Write an equation which is used to calculate the speed (vA) of the bob just before striking block B. Use the conservation of energy theorem.

One answer only.

mAgl = (1/2)mA (vA)12

mAgl = mA (vA)12

None of the above

8) Knowing (vB)2 , write an equation which is used to determine how far x the block slides before it stops. The plane is smooth and the spring has a stiffness of k and is originally unstretched.

One answer only.

mB (vB)22 = (1/2)kx2

mB (vB)22 = kx2

None of the above

Principle of Angular Impulse and Momentum

1) Determine the magnitude of the angular momentum of the 10 kg particle about point O.

H0 = ? One answer only.

60 kg.m2/s

75 kg.m2/s

90 kg.m2/s

None of the above

2) Determine the magnitude of the angular momentum of the 10 kg particle about point O.


75 kg.m2/s

100 kg.m2/s

125 kg.m2/s

None of the above

3) Calculate the angular momentum of the 10 kg particle about point O and select its value from the list.


(-200i - 100j) kg.m2/s

(-150i + 100j) kg.m2/s

(-150i - 100j) kg.m2/s

None of the above

4) Determine the magnitude of the angular impulse acting on the particle about point O. The force has a constant direction and acts for t = 2 s.

Ang. Imp = ? One answer only.

200 Nms

300 Nms

400 Nms

None of the above

5) Determine the magnitude of the angular impulse acting on the particle about point O. The force has a constant direction and acts for t = 2 s.

Ang. Imp = ? One answer only.

24 Nms

27 Nms

34 Nms

None of the above

6) The 10 kg particle slides along the smooth horizontal circular wire with an initial speed of 2 m/s. It is acted upon by a tangential 5-N force. Determine its speed when t = 2 s.


-1.5 m/s

1.5 m/s

3 m/s

None of the above

7) The 2 kg disk slides on the smooth table such that when the attached cord has a length of 3 m, the disk has a speed of 5 m/s. Compute the velocity v2 of the disk when the cord is shortened to 2 m by pulling it through the hole at O.


5 m/s

7.5 m/s

10 m/s

None of the above

Planar Kinematics of Rigid BodiesRotation About a Fixed Axis

1) A wheel, starting from rest, has an angular acceleration of α = (2t) rad/s2, where t is in seconds. Determine the wheel's angular velocity when t = 2s.

ω = ? One answer only.

2 rad/s

4 rad/s

6 rad/s

None of the above

2) cont....What is the wheel's angular displacement when t = 2s?


1.33 rad

2.66 rad

4 rad

None of the above

3) A wheel, starting from rest, has an angular acceleration of α = (4θ) rad/s2. Determine the wheel'sangular velocity when θ = 1 rad.


0 rad/s

1.5 rad/s

2 rad/s

None of the above

4) A wheel has a constant clockwise angular acceleration of α = 2 rad/s2. Determine the wheel's angular velocity at the instant t = 1 s. Initially, the wheel is rotating clockwise at 5 rad/s.


7 rad/s

9 rad/s

14 rad/s

None of the above

Chapter V

5) cont....What is the wheel's angular displacement at t = 1s?


2 rad

5 rad

7 rad

None of the above

6) The wheel starts from rest and has an angular acceleration of a = (2t) rad/s2, where t is in seconds. Determine the magnitude of the velocity of point P located on the wheel's rim at the instant t = 1 s.


0 m/s

1 m/s

2 m/s

None of the above

7) cont....What is the tangential acceleration component of point P at t = 1s?

at = ? One answer only.

1 m/s2

2 m/s2

4.2 m/s2

None of the above

8) cont....What is the normal acceleration component of point P at t = 1s?

an = ? One answer only.

1 m/s2

2 m/s2

4.2 m/s2

None of the above

9) If the angular velocity of wheel A is ωA = 2 rad/s, determine the speed of point P located on the rim of wheel B. No slipping occurs between the wheels.

vp = ? One answer only.

0 m/s

2 m/s

3 m/s

None of the above

10) If the angular velocity of wheel A is ωA = 20 rad/s, determine the speed of block C. No slipping occurs between the wheels.


1.2 m/s

2.7 m/s

3 m/s

4 m/s

None of the above Absolute General Plane Motion Analysis

1) Using geometry and/or trigonometry, relate the position coordinate x, which defines the rectilinear motion of A, to the position coordinate θ, which defines the angular motion of B.

One answer only.

x = 0.4tanθ

x = 0.4cotθ

θ = cot-1(0.4/x)

None of the above


One answer only.

x = 0.2 + 0.2tanθ

x = 0.2 + 0.2sinθ

x = 0.2 + 0.2cosθ

x = 0.4cosθ

None of the above

3) Using geometry and/or trigonometry, relate the position coordinate y, which defines the rectilinear motion of A, to the position coordinate θ, which defines the angular motion of B. Members AC and BD are each 4 m long.

One answer only.

y = 4sinθ

y = 4cosθ

y = 2sinθ + 2cosθ

y = 4tanθ

None of the above


One answer only.

(0.4)2 = x2 - 0.62

(0.4)2 = (0.6)2 + x2 - 2(0.6)xcosθ

(0.4)2 = (0.6)2 + x2 + 2(0.6)xcosθ

None of the above

5) Establish appropriate coordinates which measure the rectilinear position x of A and the angular position θ of B. Then relate these coordinates ! Cusing trigonometry and/or geometry.

One answer only.

x = 2cosθ m

x = 2tanθ m

x = 2cscθ m

None of the above

6) Establish appropriate coordinates which measure the rectilinear position x of A and the angular position θ of B. Then relate these coordinates using trigonometry and/or geometry.

One answer only.

x = 0.5cosθ m

x = 2(0.5)cosθ m

x = 2(0.5)sinθ m

x = 2(0.5)tanθ m

None of the above

7) The relation between the position x of a body and the angular position θ of another body is given. By computing the time derivative, establish a relation between ω (omega) and v, and α and a.

x = 0.6cosθ Choose 2 of the following options.

v = -ω0.6sinθ

v = ω0.6sinθ

v = 0.6sinθ

v = -0.6sinθ

a = 0.6αsinθ

a = 0.6αsinθ + 0.6ω2cosθ

a = -0.6ω2cosθ - 0.6αsinθ

a = -0.6ω2cosθ + 0.6αsinθ

8) The relation between the position x of a body and the angular position θ of another body is given. By computing the time derivative, establish a relation between ω (omega) and v, and α and a.

x = 3sinθ - 4 Choose 2 of the following options.

v = -3ωcosθ

v = 3ωcosθ

v = -3cosθ

v = 3cosθ

a = -3αcosθ

a = -3ω2sinθ + 3αcosθ

a = 3ω2sinθ + 3αcosθ

a = -3αsinθ - 3ω2cosθ Relative Motion Analysis: Velocity

1) Select from then list below the equation which represents application of vB = vA + vB/A.

One answer only.

vBi = -3j + (ωk) x (-4i + 3j)

vBi = -3j + (ωk) x (4i - 3j)

vBi = -3j + (-ωk) x (-4i + 3j)

vBi = -3j + (-ωk) x (4i - 3j)

None of the above


One answer only.

vBxi + vByj = 4i + (ωk) x (-0.3cos30i + 0.3sin30j)

vBxi + vByj = 4i + (-ωk) x (-0.3cos30i + 0.3sin30j)

vBxi + vByj = 4i + (ωk) x (0.3cos30i + 0.3sin30j)

vBxi + vByj = 4i + (-ωk) x (0.3cos30i + 0.3sin30j)

None of the above


One answer only.

vBcos30i - vBsin30j = 10i + (ωk) x (2cos20i - 2sin20j)

vBsin30i - vBcos30j = 10i + (ωk) x (2sin20i - 2cos20j)

vBsin30i - vBcos30j = 10i + (ωk) x (-2cos20i + 2sin20j)

None of the above


One answer only.

vBi = -3j + (ωk) x (2i - 1j)

vBi = -3j + (ωk) x (-2i + 1j)

-vBi = -3j + (ωk) x (2i - 1j)

-vBi = -3j + (ωk) x (-2i + 1j)

None of the above

5) Compute the velocity of point B.


0 m/s

1 m/s

2 m/s

4 m/s

None of the above



0 m/s

1 m/s

4 m/s

6 m/s

None of the above



0 m/s

1 m/s

1.41 m/s

2 m/s

None of the above Instant Centre of Zero Velocity

1) The sliding collar A has a constant velocity of 20 m/s to the right at the instant shown. Determinethe angular velocity of BC at this instant.

ωBC = ? One answer only.

27 rad/s

43 rad/s

50 rad/s

None of the above

2) The double pulley is attached to a slider block by a pin at A. If the pulleys are attached to one another and the upper cord is pulled at a speed of 12 m/s as shown, determine the velocity of the slider block.

vA = ? One answer only.

4 m/s

7.5 m/s

9 m/s

None of the above

3) The link AB has a constant angular velocity of 2 rad/s. For the position shown, determine the angular velocity of link BC.

ωBC = ? One answer only.

0 rad/s

2 rad/s

6 rad/s

None of the above Motion Analysis: Acceleration

1) Select from the list below the equation that represents the application of aB = aA + α x rB/A - ω2rB/A

One answer only.

-aBj = 2i + (αk) x (-2cos30i + 2sin30j) - (2)2(-2cos30i + 2sin30j)

-aBj = 2i + (αk) x (2cos30i - 2sin30j) - (2)2(2cos30i - 2sin30j)

-aBj = 2i + (αk) x (2cos30i + 2sin30j) - (2)2(2cos30i - 2sin30j)

-aBj = 2i + -(αk) x (2cos30i + 2sin30j) - (2)2(2cos30i - 2sin30j)

None of the above


One answer only.

(aB)xi + (aB)yj = 2i + (-3k) x (-0.2j) + (4)2(0.2j)

(aB)xi + (aB)yj = 2i + (-3k) x (0.2j) - (4)2(0.2j)

(aB)xi + (aB)yj = 2i + (3k) x (-0.2j) - (4)2(-0.2j)

(aB)xi + (aB)yj = 2i + (3k) x (0.2j) - (4)2(0.2j)

None of the above


One answer only.

4i + (aB)yj = 2i + (αk) x (-1i - 1j) + (1.41)2(-1i - 1j)

(aB)xi + (aB)yj = 2i + (-αk) x (-1i - 1j) + (1.41)2(-1i - 1j)

None of the above

4) Compute the angular acceleration of member AB. The angular velocity of the member is ω = 0.5 rad/s as shown in the figure.

α = ? One answer only.

0 rad/s2

1 rad/s2

2 rad/s2

None of the above

5) Determine the angular acceleration of member AB. At the instant considered the member has noangular velocity.

α = ? One answer only.

0.2 rad/s2

0.4 rad/s2

0.8 rad/s2

None of the above

Planar Kinetics of Rigid Body: Force & acc.

Mass Moment of Inertia

1) The radius of gyration of the 10kg body about an axis passing through point G and directed perpendicular to the page is kG = 2m. Determine the moment of inertia of the body about an axis passing through point A and directed perpendicular to the page.

IA = ? One answer only.

40 kgm2

120 kgm2

160 kgm2

200 kgm2

2) The moment of inertia of the 2kg slender rod about an axis passing through its mass centre is determined from IG = (1/12) mL2. Apply the parallel-axis theorem in order to determine the moment of inertia about an axis passing through the pin at A.


6 kgm2

24 kgm2

18 kgm2

19.5 kgm2

3) The moment of inertia of the 10kg disk about an axis passing through its mass centre is I = mr2/2. Determine the moment of inertia of the disk about an axis passing through the pin at A.

Chapter VI


20 kgm2

40 kgm2

60 kgm2

80 kgm2

Equations of Motion: Translation

1) The cart has a mass 100kg and a mass centre at G. Determine its acceleration.

a = ? m/s2

Type your answer in the textarea below.

2) cont.... How far will the cart travel to attain a velocity of 4m/s starting from rest?

s = ? m


3) The 100kg bar is pinned at A and is subjected to an acceleration of 3m/s2. Use a single equation of motion and determine the tension in the cord.

T = ? N


4) cont.... How much time does it take for the rod to attain a speed of 9m/s starting from rest?

t = ? s


Equations of Motion: Rotation about a Fixed Axis

1) The disk has a mass of 100kg. Determine its angular acceleration in t = 2s starting from rest.

α = ?

One answer only.

1 rad/s2

2 rad/s2

4 rad/s2

8 rad/s2

2) cont....What is the angular velocity of the disk in t = 2s?

ω = ? rad/s


3) Determine the angular acceleration of the 100kg slender rod at the instant shown. The bar is initially at rest.

α = ?

One answer only.

0 rad/s2

6 rad/s2

12 rad/s2

24 rad/s2

4) cont....What is the horizontal reaction at the pin A?

AX = ?

One answer only.

0 N

300 N

600 N

1200 N

5) cont....What is the vertical reaction at the pin?

AY = ?


Equations of Motion: General Plane Motion

1) The rod has a mass of 100kg and is originally at rest. Determine the acceleration of its mass centre at the instant shown.

aG = ?

One answer only.

1 m/s2

2 m/s2

3 m/s2

4 m/s2

2) cont....What is the bar's angular acceleration?

α = ?

One answer only.

1.5 rad/s2

3 rad/s2

6 rad/s2

9 rad/s2

3) The disk has a mass of 100kg. If it rolls without slipping, determine its angular acceleration. For the solution sum moments about the ground point A and use kinematics.

α = ?

One answer only.

0 rad/s

2 rad/s

3 rad/s

6 rad/s

4) cont.... If the surface at A is smooth, what is the acceleration at point G on the disk?

aG = ?

One answer only.

0 m/s2

1.5 m/s2

3 m/s2

6 m/s2

5) contd.... What is the angular acceleration?

d = ?

One answer only.

0 rad/s2

2 rad/s2

3 rad/s2

6 rad/s2

6) The 100kg disk is subjected to a couple moment of 100Nm. If the coefficient of kinetic friction at A is µA = 0.1, determine the acceleration of its mass centre. The disk slips as it rolls.

aG = ?

One answer only.

0.981 m/s2

1.962 m/s2

2 m/s2

9.81 m/s2

Principles of Work and Energy .

1) The 10kg rod has a moment of inertia which is computed from IG = (1/12)mL2. If it is rotating at ω = 2 rad/s, determine its kinetic energy when it is computed about the mass centre G.

TG = ?

One answer only.

15 J

30 J

45 J

60 J

2) cont.... What is the rod's kinetic energy when it is computed about the fixed point at rotation, O?

TO = ?

One answer only.

15 J

30 J

45 J

60 J

3) Compute the kinetic energy of the 100kg block if it has the motion shown.

Chapter VII

T = ? J


4) Compute the kinetic energy of the 100kg disc if it has the motion shown.

T = ?

One answer only.

225 J

25 J

50 J

75 J

5) Compute the kinetic energy of the 100kg disc if it has the motion shown.

T = ?

One answer only.

12.5 J

25 J

50 J

75 J

6) Compute the work done by the indicated force when block undergoes the specified displacement.

U = ?

One answer only.

0 J

169.9 J

981 J

1962 J

7) Compute the work done by the indicated force when the disk undergoes the specified displacement.

U = ?

One answer only.

50 J

100 J

200 J

400

8) Compute the work done by the indicated couple moment when the disk undergoes the specified displacement.

U = ? J


9) Compute the work done by the indicated force when the disk undergoes the specified displacement.

U = ? J


10) ) Compute the work done by the indicated force when the disk undergoes the specified displacement.

U = ? J


11) Compute the work done by the indicated force when the block undergoes the specified displacement.

U = ? J


12) Compute the work done by the indicated force when the block undergoes the specified displacement.

U = ? J


13) Select from the list below the equation which represents the reduced form of the equation of work and energy for the 10kg bar. The bar has the initial motion shown and displaces θ = 90o.

One answer only.

9.81 = 6.67ω2

35.2 = 6.67ω2

158.1 = 6.67ω2

60.0 = 6.67ω2

14) Select from the list below the equation which represents the reduced form of the equation of work and energy from the 10kg disc. The disk has the initial motion shown and displaces s = 2m

One answer only.

10 = ω2

6 = ω2

20 = ω2

30 = ω2

15) Select from the list below the equation which represents the reduced form of the equation of work and energy for the 10kg disk. The disk has the initial motion shown and displaces s = 1m.

One answer only.

120 = 30ω2

240 = 30ω2

98.1 = 30ω2

218.1 = 30ω2

Conservation of Energy

1) Compute the potential energy of the rigid block with respect to the datum, when it is in the position shown.

V = ? J


2) Compute the potential energy of the rigid block with respect to the datum when it is in the position shown.

V = ? J


3) Compute the potential energy of the rigid block with respect to the datum, when it is in the position shown.

V = ? J


4) Compute the potential energy of the rigid bidy with respect to the datum, when it is in the position shown.

V = ? J


5) Select from the list below the equation which represents the reduced form of the conservation of energy theorem for the 10kg rod. The rod has the initial motion shown and displaces θo. Use the datum shown.

One answer only.

158.1 = 6.67ω2

60 = 98.1 + 6.67ω2

203.1 = 98.1 + 26.67ω2

105 = 98.1 + 26.67

6) Select from the list below the equation which represents the reduced form of the conservation of energy for the 10kg disk. The disk has the initial motion shown and displaces 1m. Use the datum shown.

One answer only.

80 = 30ω2

120 = 98.1 + 30ω2

40 = 98.1 + 10ω2

80 = 98.1 + 20ω2

7) Select from the list below the equation which represents the reduced form of the conservation of energy for 10kg rod. The rod is released from the rest and displaces θ = 45o. Use the datum shown and neglect the mass of the rollers at A and B.

One answer only.

98.1 = 13.34ω2

98.1 = 6.67ω2

98.1 = 11.67ω2

98.1 = 26.64ω2

Principles of Impulse and Momentum

1) The slender rod has a mass of 100kg and is moving as shown. Compute the magnitude of its linear momentum aboutpoint O.

L = ? kgm/s


2) cont....Compute the magnitude of its angular momentum about point O.

Ho = ? kgm2/s


3) The disk has a mass of 100kg and is moving as shown. Compute the magnitude of its linear movement about the point O.

L = ? kgm/s


4) cont.... Compute the magnitude of its angular momentum about the point O.

Ho = ? kgm2/s


Chapter VIII

5) The disk has a mass of 100kg and is moving as shown. Compute the magnitude of its linear momentum about the point O.

L = ? kgm/s


6) cont.... Compute the magnitude of its angular momentum about the point O.

Ho = ? kgm2/s


7) The disk has a mass of 10kg. If it is acted upon by the 60Nm couple moment, determine the angular velocity of thedisk in t = 2s starting from rest. No slipping occurs.

ω = ? rad/s


8) The disk has a mass of 10kg. If it is acted upon by the horizontal force of variable magnitude, determine the angular velocity of the disk in t = 2s starting from rest. No slipping occurs. "

ω = ? rad/s


9) The spool has a mass of 10kg and a radius of gyration KG = 1m. If it is acted by the horizontal force, determine the angular velocity of the spool in t = 5s starting from rest. The surface at A is smooth.

ω = ? rad/s


10) The disk has a mass of 10kg. If it is released from rest, determine its angular velocity in t = 3s.

One answer only.

ω = 19.62 rad/s

ω = 9.81 rad/s

None of the above

Chapter I Kinematics of Particle.

Rectilinear KinematicsQ1 Q2 Q3 Q4 Q5 Q6 Q7

Graphical SolutionsQ1 Q2 Q3 Q4 Q5 Q6 Q7

Curvilinear motion Rect. Coord.Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10Q11 Q12

Curvilinear motion: Normal & tang. Coord.Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8

Curvilinear motion: Cyl. Coord.Q1 Q2 Q3 Q4 Q5 Q6

Dependant & rel. motion analysis:Q1 Q2 Q3 Q4 Q5 Q6

Chapter IIKinetics of particle: Force & Accl.

Equations of Motion: Rect. Coor.Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8

Equations of Motion: Normal & Tgt Coord..Q1 Q2 Q3 Q4 Q5 Q6

Equations of Motion: Cyl. Coord.Q1 Q2 Q3 Q4 Q5

Chapter III Kinetics of a particle: Work & Energy

Principle of work & energyQ1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10Q11

Power & EfficiencyQ1 Q2 Q3 Q4 Q5 Q6 Q7

Conservation of Energy TheoremQ1 Q2 Q3 Q4 Q5 Q6

Chapter IV Kinetics of a Particle: Impulse & momentum

Principle of linear impulse & momentumQ1 Q2 Q3 Q4 Q5 Q6 Q7 Q8

Conservation of linear momentumQ1 Q2 Q3 Q4 Q5 Q6 Q7

ImpactQ1 Q2 Q3 Q4 Q5 Q6 Q7 Q8

Principal of angular impulse & momentumQ1 Q2 Q3 Q4 Q5 Q6 Q7

Chapter V Plane Kinematics of rigid bodies

Rotation about fixed axisQ1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10

Absolute general plane motion analysis

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8

Relative motion analysis:VelocityQ1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10

Instantaneous centre of zero velocityQ1 Q2 Q3 Q4 Q5

Relative motion analysis: AccelerationQ1 Q2 Q3 Q4 Q5

Chapter VI Plane Kinetics of rigid body: F & A.Mass moment of inertiaQ1 Q2 Q3

Equtions of motion: TranslationQ1 Q2 Q3 Q4

Equtions of motion: Rotation about fixed axisQ1 Q2 Q3 Q5 Q5

Equtions of motion:General plane motionQ1 Q2 Q3 Q4 Q5 Q6

Chapter VII Plane kinetics of rigid body: Work & Energy

Principle of work & energyQ1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10Q11 Q12 Q13 Q14 Q15

Conservation of energyQ1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10

Chgapter VIIIPlanar kinetics of a rigid body : W & EPrinciple of impulse & momentum

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