Copyright © 2012 Pearson Education Inc. Application of Newton’s laws: free body diagram Physics 7C lecture 03 Thursday October 3, 8:00 AM – 9:20 AM Engineering.

Copyright © 2012 Pearson Education Inc.

Application of Newton’s laws: free body diagram

Physics 7C lecture 03

Thursday October 3, 8:00 AM – 9:20 AMEngineering Hall 1200


Newton’s laws

• Newton’s First Law of Motion: when forces are balanced the object will keep its motion/velocity.

• Newton’s Second Law of Motion: F = m a, force causes changes to the motion/velocity.

• Newton’s Third Law of Motion: action-reaction pairs

• Yet: The laws are simple to state but intricate in their application.

• Let’s do some iClicker questions first.

© 2012 Pearson Education, Inc.

Q4.1

v

Motor

Cable

Elevator

An elevator is being lifted at a constant speed by a steel cable attached to an electric motor. There is no air resistance, nor is there any friction between the elevator and the walls of the elevator shaft.

The upward force exerted on the elevator by the cable is

A. greater than the downward force of gravity.

B. equal to the force of gravity.

C. less than the force of gravity.

D. any of the above, depending on the speed of the elevator.


A4.1

v

Motor

Cable

Elevator

An elevator is being lifted at a constant speed by a steel cable attached to an electric motor. There is no air resistance, nor is there any friction between the elevator and the walls of the elevator shaft.







Q4.2

v

Motor

Cable

Elevator

An elevator is being lowered at a constant speed by a steel cable attached to an electric motor. There is no air resistance, nor is there any friction between the elevator and the walls of the elevator shaft.







A4.2

v

Motor

Cable

Elevator

An elevator is being lowered at a constant speed by a steel cable attached to an electric motor. There is no air resistance, nor is there any friction between the elevator and the walls of the elevator shaft.







Q4.5

A. crate A exerts more force on crate B than B exerts on A

B. crate A exerts less force on crate B than B exerts on A

C. crate A exerts as much force on crate B as B exerts on A

D. Answer depends on the details of the friction force

If the two crates are accelerating to the right,

ABF

A lightweight crate (A) and a heavy crate (B) are side-by-side on a horizontal floor. You apply a horizontal force F to crate A. There is friction between the crates and the floor.


A4.5

A. crate A exerts more force on crate B than B exerts on A

B. crate A exerts less force on crate B than B exerts on A

C. crate A exerts as much force on crate B as B exerts on A

D. Answer depends on the details of the friction force

If the two crates are accelerating to the right,

ABF

A lightweight crate (A) and a heavy crate (B) are side-by-side on a horizontal floor. You apply a horizontal force F to crate A. There is friction between the crates and the floor.


Q4.6

v

Motor

Cable

Elevator

An elevator is being lowered at constant speed by a steel cable attached to an electric motor. There is no air resistance, nor is there any friction between the elevator and the walls of the elevator shaft.

The upward force exerted on the elevator by the cable has the same magnitude as the force of gravity on the elevator, but points in the opposite direction. Why?

A. Newton’s first law

B. Newton’s second law

C. Newton’s third law


A4.6

v

Motor

Cable

Elevator

An elevator is being lowered at constant speed by a steel cable attached to an electric motor. There is no air resistance, nor is there any friction between the elevator and the walls of the elevator shaft.

The upward force exerted on the elevator by the cable has the same magnitude as the force of gravity on the elevator, but points in the opposite direction. Why?

A. Newton’s first law

B. Newton’s second law

C. Newton’s third law


Q4.3

The graph to the right shows the velocity of an object as a function of time.

Which of the graphs below best shows the net force versus time for this object?

t

vx

0

A. B. C. D. E.

t

Fx

0 t

Fx

0 t

Fx

0 t

Fx

0 t

Fx

0


A4.3

The graph to the right shows the velocity of an object as a function of time.

Which of the graphs below best shows the net force versus time for this object?

t

vx

0

A. B. C. D. E.

t

Fx

0 t

Fx

0 t

Fx

0 t

Fx

0 t

Fx

0


Free-body diagrams

• A free-body diagram is a sketch showing all the forces acting on an object.

• Why do we need it?

What is the tension force in the rope?


Free-body diagrams

• We need to isolate the objects and study the forces on each of them.

T1W1

T1

W2

T2

T2

W3Note: W = m gaction-reaction pairs


Free-body diagrams

• We can apply the 2nd law to each of the following, or to the group.

T1W1

T1

W2

T2

T2

W3

The three objects share the same acceleration:a = (F-W1-W2-W3) / (m1+m2+m3) = F/(m1+m2+m3) – g = 200/(6+4+5) – 9.8 = 3.53 m/s2


Free-body diagrams

• Now we focus on m1 and solve for tension T1.

T1W1

for the upper mass, apply the 2nd law:

F-W1-T1 = m1 awe have:

T1 = F-W1-m1 a = 200-6*9.8-6*3.53 = 120.02 N


Free-body diagrams

• Similarly we focus on the rope and solve for tension T2.

T1

W2

T2

T1-W2-T2 = m2 awe have:

T2 = T1-W2-m2 a = 120.02-4*9.8-4*3.53 = 66.7 N


Free-body diagrams

• We can double check the result on the lower mass:

T2

W3

T2-W3 = m3 a

we have calculated: T2 = 66.7 N a = 3.53 m/s2

66.7 – 5*9.8 = 5 * 3.53 ?

true!


Free-body diagrams—examples








Q4.9

A person pulls horizontally on block B, causing both blocks to move horizontally as a unit. There is friction between block B and the horizontal table.

If the two blocks are moving to the right at constant velocity,

A. the horizontal force that B exerts on A points to the left.

B. the horizontal force that B exerts on A points to the right.

C. B exerts no horizontal force on A.

D. not enough information given to decide


A4.9

A person pulls horizontally on block B, causing both blocks to move horizontally as a unit. There is friction between block B and the horizontal table.

If the two blocks are moving to the right at constant velocity,

A. the horizontal force that B exerts on A points to the left.

B. the horizontal force that B exerts on A points to the right.

C. B exerts no horizontal force on A.



A woman pulls on a 6.00-kg crate, which in turn is connected to a 4.00-kg crate by a light rope. The light rope remains taut.

A. is subjected to the same net force and has the same acceleration.

B. is subjected to a smaller net force and has the same acceleration.

C. is subjected to the same net force and has a smaller acceleration.

D. is subjected to a smaller net force and has a smaller acceleration.

E. none of the above

Q4.12

Compared to the 6.00-kg crate, the lighter 4.00-kg crate


A woman pulls on a 6.00-kg crate, which in turn is connected to a 4.00-kg crate by a light rope. The light rope remains taut.

A. is subjected to the same net force and has the same acceleration.

B. is subjected to a smaller net force and has the same acceleration.

C. is subjected to the same net force and has a smaller acceleration.

D. is subjected to a smaller net force and has a smaller acceleration.

E. none of the above

A4.12

Compared to the 6.00-kg crate, the lighter 4.00-kg crate


A car engine is suspended from a chain linked at O to two other chains. Which of the following forces should be included in the free-body diagram for the engine?

A. tension T1

B. tension T2

C. tension T3

D. two of the above

E. T1, T2, and T3

Q5.1


A car engine is suspended from a chain linked at O to two other chains. Which of the following forces should be included in the free-body diagram for the engine?

A. tension T1

B. tension T2

C. tension T3

D. two of the above

E. T1, T2, and T3

A5.1


Two-dimensional equilibrium

• A car engine hangs from several chains.


Two-dimensional equilibrium

• A car engine hangs from several chains.


Q5.3

When released, the cart accelerates up the ramp.

Which of the following is a correct free-body diagram for the cart?

A. B. C. D.

m1a m1aw1 w1 w1 w1

T T T Tn n n n

A cart (weight w1) is attached by a lightweight cable to a bucket (weight w2) as shown. The ramp is frictionless.


A5.3

When released, the cart accelerates up the ramp.

Which of the following is a correct free-body diagram for the cart?

A. B. C. D.

m1a m1aw1 w1 w1 w1

T T T Tn n n n

A cart (weight w1) is attached by a lightweight cable to a bucket (weight w2) as shown. The ramp is frictionless.


Q5.4

A. T = w2

B. T > w2

C. T < w2


When released, the cart accelerates up the ramp and the bucket accelerates downward. How does the cable tension T compare to w2?

A cart (weight w1) is attached by a lightweight cable to a bucket (weight w2) as shown. The ramp is frictionless. The pulley is frictionless and does not rotate.


A5.4

A. T = w2

B. T > w2

C. T < w2


When released, the cart accelerates up the ramp and the bucket accelerates downward. How does the cable tension T compare to w2?

A cart (weight w1) is attached by a lightweight cable to a bucket (weight w2) as shown. The ramp is frictionless. The pulley is frictionless and does not rotate.


Bodies connected by a cable and pulley

• If the cart is moving at constant speed, what is w2/w1?




consider the bucketT = w2




consider the cart along x direction:W1 Sin 15o – T = 0

Thus: W2 = W1 Sin 15o

and: W2/W1 = Sin 15o = 0.26

Copyright © 2012 Pearson Education Inc. Application of Newton’s laws: free body diagram Physics 7C lecture 03 Thursday October 3, 8:00 AM – 9:20 AM Engineering.

Documents

motor cable elevator

friction force

elevator shaft

upward force

downward force of gravity

horizontal force f

force causes changes

steel cable