DESCRIBING MOTION

DYNAMICS• branch of mechanics that deals with the

study of bodies that are in motion • Branches: Kinematics and Kinetics

KINEMATICS vs KINETICS

• is a study under dynamics which deals with the space-time relationships in bodies that are in motion.

• It is the quantitative description of motion used to determine some unknown property of the motion.

deals with the study of the kind of motion of body due to the action of forces

Describing Motion

• a continuous change of position with respect to a specific frame of reference during a given time

• Everything moves with respect to or relative to a certain reference point.

Describing Motion• Rectilinear Motion

– kinematics of bodies that are moving along a straight path

SCALAR AND VECTOR QUANTITIES

MOTION - a continuous change of position with respect to a specific frame of reference during a given time.

 

RECTILINEAR MOTION - kinematics of bodies that are moving along either a straight path.

DISPLACEMENT, D

D = final position - initial position

D = X2 -X1

defined as a vector that points

from an objects’ initial position to its final position and whose magnitude equals the distance separating the points.

 

DISTANCE,d

the position of the object as measured from a reference point.

 

SPEED AND VELOCITY

VELOCITY

Velocity (v), is the displacement of an object during a certain time divided by that time.

 

Average velocity v of an object during some time period is the object’s displacement ( a vector) during that time divided by the time.

 

v = displacement / elapsed time = D / t

SPEED- the scalar magnitude of the velocity.

- total distance traveled per unit time.

SPEED

Average speed , is defined as the distance traveled divided by the time

required to travel that distance.

 

= distance traveled / elapsed time

= d / t

INSTANTANEOUS SPEED

indicates only how fast an object is moving at each instant of time. (the speedometer of an automobile

indicates its instantaneous speed)

INSTANTANEOUS VELOCITY

indicates how fast an object moves at each instant of time and the direction of that motion.

 

ACCELERATION  

Acceleration, a , is the change in an object’s velocity divided by the time required for that

change.

Deceleration is a decrease in the speed of an object.

 

a = change in velocity/ elapsed time

a = vf-vi/ t

where :a is the acceleration

vf is the final velocity

vI is the initial velocityt is the time interval or time elapsed

 

Sign Convention for Acceleration

Acceleration is positive (+)if V2 is greater than V1.  

Acceleration, on the other hand, is negative (-) if V2 is lesser than V1.

VELOCITY AND ACCELERATION

Three factors that affect acceleration:

(1)  the change in the magnitude of the object’s

velocity - that is, its change in speed

(2) the change in the direction of the object’s

velocity

(3) the time required for these changes.

 

Sample Problems

1. What is the average speed of a horse that gallops 100 m in 8 s? How about if it gallops 50 m in 4 s?

2. If a car travels with an average speed of 60 km/h for an hour, it will cover a distance of 60 km. (a) How far would the car travel if it moved at this rate for 4 h? (b) for 10 h?

3. Calculate the average speed of a tennis ball that travels the full length of the court, 24m, in 0.5 s.

4. Calculate the acceleration of a ball that starts from rest and rolls down a ramp and gains a speed of 25 m/s in 5 s.

 KINEMATIC EQUATION FOR UNIFORMLY ACCELERATED

RECTILINEAR MOTION

1) Vf = Vo + at

2) Vave = Vo + Vf

2 

3) ∆x = Vot + at2

2  

4) Vf2 = Vo

2 + 2a∆x

Sample Problems

5. A car starting from rest is accelerated by 8 m/sec2 to the right. Find (a) the velocity at the end of 5 sec., and (b) displacement covered during this period.

6. A car starts from rest and accelerates 8 m/sec2. How far will it travel after 4 sec?

FREELY FALLING BODIES

• a body is said to be in free fall if gravity or earth’s pull is the only force acting on it.

• if air resistance is neglected, it is found that falling bodies are accelerated toward the earth’s surface.

FREELY FALLING BODIES

• all equations for linear motion will therefore be applicable.

• the acceleration is due to gravity (g) whose direction is toward the center of the earth.

The value of gapproximately equal to

9.8 m/sec2, or 980 cm/sec2, or 32 ft/sec2.

Two situations to be considered when solving problems involving g:

(1) when the object’s motion is in the direction of g, (i.e., free fall).

When the object is allowed to fall, the direction of the motion is downward and it is with the direction of g.

- consider the downward motion as positive and we take g as positive.

(2) when the object’s motion is in opposite direction of g, (i.e., a ball thrown upward).

When the object is thrown vertically upward, the direction of the motion is upward and it is opposite the direction of g, therefore g becomes negative.

EQUATIONS OF FREE FALL

 KINEMATIC EQUATION FOR FREE FALL

1) Vf = Vo + gt

2) Vave = Vo + Vf

2  3) ∆Y = Vot + gt2

2   4) Vf

2 = Vo2 + 2g∆Y

1. A body is released from rest and falls freely. Determine its position and velocity after 2 sec.

2. A body falls freely from rest. Find its speed after falling 70 m.

EFFECT OF WEIGHT AND AIR RESISTANCE

• Weight has no effect on the acceleration of bodies in free fall.

• Both will have the same acceleration

due to gravity.

EFFECT OF WEIGHT AND AIR RESISTANCE

• Frictional force due to air resistance affects the motion of objects under free fall. Frictional force or drag due to air resistance can not be ignored.

• When the drag force and the downward pull

of gravity are balanced, the velocity of object remains constant. This constant velocity is called terminal velocity.

Practice Exercise

• A body falls freely from rest. Find (a) its acceleration); (b) the distance it falls at 3 s; (c) its speed after falling 75 m; (d) the time required to reach a speed of 25 m/s; and (e) the time it takes to fall 300 m.