PHYS1001 Chapter Notes - Chapter all: Net Force, Centripetal Force, Acceleration

which of the vectors below best represents the direction of the impulse vector j⃗ ?

To learn about the impulse-momentum theorem and its applications in some common cases.

Using the concept of momentum, Newton's second law can be rewritten as

?F? =dp? dt, (1)

where ?F?  is the net force F? net acting on the object, and dp? dt is the rate at which the object's momentum is changing.

If the object is observed during an interval of time between times t1 and t2, then integration of both sides of equation (1) gives

?t2t1?F? dt=?t2t1dp? dtdt. (2)

The right side of equation (2) is simply the change in the object's momentum p2??p1?. The left side is called the impulse of the net force and is denoted by J? . Then equation (2) can be rewritten as

J? =p2??p1?.

This equation is known as the impulse-momentum theorem. It states that the change in an object's momentum is equal to the impulse of the net force acting on the object. In the case of a constant net force F? net acting along the direction of motion, the impulse-momentum theorem can be written as

F(t2?t1)=mv2?mv1. (3)

Here F, v1, and v2 are the components of the corresponding vector quantities along the chosen coordinate axis. If the motion in question is two-dimensional, it is often useful to apply equation (3) to the x and y components of motion separately.

( The following questions will help you learn to apply the impulse-momentum theorem to the cases of constant and varying force acting along the direction of motion. First, let us consider a particle of mass m moving along the x-axis. The net force F is acting on the particle along the x-axis. F is a constant force.)

A) The particle starts from rest at t=0. What is the magnitude p of the momentum of the particle at time t? Assume that t>0.

B) The particle starts from rest at t=0. What is the magnitude v of the velocity of the particle at time t? Assume that t>0.

C) The particle has the momentum of magnitude p1 at a certain instant. What is p2, the magnitude of its momentum ?t seconds later?

D) The particle has the momentum of magnitude p1 at a certain instant. What is v2, the magnitude of its velocity ?t seconds later?

E) Find the magnitude of the impulse J delivered to the particle.

F) Which of the vectors below best represents the direction of the impulse vector J??
(Figure 1)

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Question 1 of 7 0.5 Points
A 6 N force acts on a 0.3-kg object for 0.3 seconds. By how muchdoes the object's momentum change (in kg-m/s)?

Question 2 of 7 0.5 Points
A 0.4-kg object is traveling to the right (in the positivedirection) with a speed of 1 m/s. After a 0.2 s collision, theobject is traveling to the left at 3 m/s. What is the magnitude ofthe impulse (in N-s) acting on the object? The answer must bepositive.

Question 3 of 7 1.0 Points
The force shown in the attached figure is the net eastward forceacting on a ball. The force starts rising at t = 0.020 s, fallsback to zero at t = 0.062 s, and reaches a maximum force of 55 N atthe peak. Determine with an error no bigger than 25% (high or low)the magnitude of the impulse (in N-s) delivered to the ball. Hint:Do not use J = F?t. Look at the figure. Find the area of a nearlyequally sized triangle.

Question 4 of 7 1.0 Points
A bat hits a moving baseball. If the bat delivers a net eastwardimpulse of 0.6 N-s and the ball starts with an initial horizontalvelocity of 3.8 m/s to the west and leaves with a 5.2m/s velocityto the east, what is the mass of the ball (in grams)?
Part 5 of 7 -

Question 5 of 7 0.5 Points
The force sensor measures the force on the sensor due to thebumper, but the cart's momentum change arises from the force on thecart due to the bumper. Which of the following facts are needed toassert that the magnitude of these two forces are nearly equal atall times.
1. Their magnitudes differ by the magnitude of the net force on thebumper.
2. The force of friction is small.
3. The net force on the bumper is small.
4. The cart's weight is canceled by the the normal force exerted bythe track.

A. 1, 3

B. 2, 4

C. 3, 4

D. 1, 2

E. 1, 4

F. 1, 2, 3, 4

G. 2, 3

Part 6 of 7 -

Question 6 of 7 1.0 Points
A cart traveling at 0.3 m/s collides with stationary object. Afterthe collision, the cart rebounds in the opposite direction. Thesame cart again traveling at 0.3 m/s collides with a differentstationary object. This time the cart is at rest after thecollision. In which collision is the impulse on the cartgreater?

A. The second collision.

B. Cannot be determined without knowing the mass of the cart.

C. The impulses are the same.

D. The first collision.

E. Cannot be determined without knowing the rebound speed of thefirst collision. Reset Selection

Part 7 of 7 -

Question 7 of 7 0.5 Points
The force vs. time graphs for two collisions are shown. Whichcollision has the largest impulse?


A. The impulse for collision 2 since it lasts longer.

B. Cannot be determined since the masses are unknown.

C. The impulse for collision 1 since it has the larger maximumforce.

D. Cannot be determined since the initial an final speeds areunknown.

E. The impulses are the same.

Question 1 of 7 0.5 Points
A 6 N force acts on a 0.3-kg object for 0.3 seconds. By how muchdoes the object's momentum change (in kg-m/s)?

Question 2 of 7 0.5 Points
A 0.4-kg object is traveling to the right (in the positivedirection) with a speed of 1 m/s. After a 0.2 s collision, theobject is traveling to the left at 3 m/s. What is the magnitude ofthe impulse (in N-s) acting on the object? The answer must bepositive.

Question 3 of 7 1.0 Points
The force shown in the attached figure is the net eastward forceacting on a ball. The force starts rising at t = 0.020 s, fallsback to zero at t = 0.062 s, and reaches a maximum force of 55 N atthe peak. Determine with an error no bigger than 25% (high or low)the magnitude of the impulse (in N-s) delivered to the ball. Hint:Do not use J = F?t. Look at the figure. Find the area of a nearlyequally sized triangle.

Question 4 of 7 1.0 Points
A bat hits a moving baseball. If the bat delivers a net eastwardimpulse of 0.6 N-s and the ball starts with an initial horizontalvelocity of 3.8 m/s to the west and leaves with a 5.2m/s velocityto the east, what is the mass of the ball (in grams)?
Part 5 of 7 -

Question 5 of 7 0.5 Points
The force sensor measures the force on the sensor due to thebumper, but the cart's momentum change arises from the force on thecart due to the bumper. Which of the following facts are needed toassert that the magnitude of these two forces are nearly equal atall times.
1. Their magnitudes differ by the magnitude of the net force on thebumper.
2. The force of friction is small.
3. The net force on the bumper is small.
4. The cart's weight is canceled by the the normal force exerted bythe track.

A. 1, 3

B. 2, 4

C. 3, 4

D. 1, 2

E. 1, 4

F. 1, 2, 3, 4

G. 2, 3

Part 6 of 7 -

Question 6 of 7 1.0 Points
A cart traveling at 0.3 m/s collides with stationary object. Afterthe collision, the cart rebounds in the opposite direction. Thesame cart again traveling at 0.3 m/s collides with a differentstationary object. This time the cart is at rest after thecollision. In which collision is the impulse on the cartgreater?

A. The second collision.

B. Cannot be determined without knowing the mass of the cart.

C. The impulses are the same.

D. The first collision.

E. Cannot be determined without knowing the rebound speed of thefirst collision. Reset Selection

Part 7 of 7 -

Question 7 of 7 0.5 Points
The force vs. time graphs for two collisions are shown. Whichcollision has the largest impulse?


A. The impulse for collision 2 since it lasts longer.

B. Cannot be determined since the masses are unknown.

C. The impulse for collision 1 since it has the larger maximumforce.

D. Cannot be determined since the initial an final speeds areunknown.

E. The impulses are the same.