Post on 21-Dec-2015
Chapter 13
Dynamics
Chapter 3 Newton’s Law
NEWTON'S LAW OF INERTIA A body, not acted on by any force, remains in
uniform motion. NEWTON'S LAW OF MOTION
Moving an object with twice the mass will require twice the force.
Force is proportional to the mass of an object and to the acceleration (the change in velocity).
F=ma.
W = m*g
Fnet = F = T1 + T2 + T3 = 0
x- and y-components:T1x = - T1 cos 37o = - 0.8 T1T1y = T1 sin 37o = 0.6 T1T2x = T2 cos 53o = 0.6 T2T2y = T2 sin 53o = 0.8 T2
Solve for tension T1 and T2.Fnet,x = F x = T1 x + T2 x + T3 x = 0T1 x + T2 x + T3 x = 0- 0.8 T1 + 0.6 T2 + 0 = 0
T1 = 0.75 T2
Dynamics
M1: up as positive:Fnet = T - m1*g = m1 a1
M2: down as positive.Fnet = F = m2*g - T = m2 a2
3. Constraint equation:a1 = a2 = a
Equations
From previous:T - m1*g = m1 a
T = m1 g + m1 a Previous for Mass 2:m2*g - T = m2 a
Insert above expr. for Tm2 g - ( m1 g + m1 a ) = m2 a
( m2 - m1 ) g = ( m1 + m2 ) a( m1 + m2 ) a = ( m2 - m1 ) g
a = ( m2 - m1 ) g / ( m1 + m2 )
Rules1. Free-Body Analysis, one for each mass + Newton’s Law
3. Algebra:Solve system of equations for all unknowns
2. Constraint equation(s): Define connections.You should have as many equations as Unknowns.COUNT!
0 = 30 0
g
i
J
m
M*g
M*g*sin
-M*g*cosj
Mass m rests on the 30 deg. Incline as shown. Step 1: Free-Body Analysis. Best approach: use coordinates tangential and normal to the path of motion as shown.
Mass m rests on the 30 deg. Incline as shown. Step 1: Free-Body Analysis.
Step 2: Apply Newton’s Law in each Direction:
0 = 30 0
g
i
J
m
M*g
M*g*sin
-M*g*cosj
xmxForces *i*sin*g*m)_(
)_(0j*cos*g*m-N )_( onlystaticyForces
N
Friction F = k*N:Another horizontal
reaction is added in negative x-direction.
0 = 30 0
g
i
J
m
M*g
M*g*sin
-M*g*cosj
xmNkxForces *i*)*sin*g*m()_(
)_(0j*cos*g*m-N )_( onlystaticyForces
N k*N
Midterm 1 :Some suggestions
•Systematic work: it takes practice, lots of it.
•Passive understanding is good, yet you still must train yourself through active practice.
•It’s all mathematical: Practice calculus and analytical geometry!
Midterm 1:Suggestions cont’d
•‘Deep Thinking 1’: Map the solution path BEFORE starting the analysis.
‘Deep Thinking 2’: Select the laws you will use.
•‘Deep Thinking 3’: Map out the Connections between the laws that will lead to the answer.
Preparing for Exam 1
•Modeling: Free-Body Analysis
•Laws and Definitions: Laws of Kinematics, Terms such as , Coriolis accel, Moving Frames of Ref.
•Seek to understand the concepts
•Practice problem solving. Copying the homework gives you an illusion and useless points
Multiple Masses A and B move in i and j-directions.
Steps: 1. Write Newton for
each Mass.2. Constraint equation
connects both masses. Here:
30 deg.
g
x
y60 deg.
vA = - vB
fig_03_007
Newton’s Law for Rotation
rramF *
amF *
Step 1: Free-Body Analysis
Step 2: Newton in radial and tangential directions
Rotation Kinematics
Similar to translation:
dt*
dt*
and dd **