# LAB: Ballistic Pendulum + Conservation of Momentum

I'm doing the prelab questions which require conceptual questions, not so much of math.
The experiment is a typical ballistic pendulum lab - you'd shoot a paintball twoard a pendulum bob, and you measure the height the pendulum bob reaches after collision to calculate the related velocities.

## Homework Statement

#1 Define the paintball plus pendulum bob as a system at the instant that the paintball collides with the bob. Do any external forces act on this system?
#2 Will momentum be conserved during the collision? Is any approximation involved?
#3 Will momentum be conserved while the pendulum is swinging? Explain.
#4 Since the velocity and therefore the momentum of the pendulum and ball are zero at the height h (this would be the max height), how can we say that momentum is conserved in the experiment?
#5 Comment on the following statement: "The momentum of the paintball and bob could not be conserved in this experiment because of the large frictional forces between the bob and the entering paintball."

## Homework Equations

These questions are conceptual I think but relevant equations would be
Pi = Pf
m_ball * v_ball = (m_pend + m_ball) * v_pend

## The Attempt at a Solution

#1 Define the paintball plus pendulum bob as a system at the instant that the paintball collides with the bob. Do any external forces act on this system?
-I'm not so sure what it means by define them as a system...
-I said external forces would be gravity and air resistance (friction)

#2 Will momentum be conserved during the collision? Is any approximation involved?
-I said yes, conserved.
-I'm not sure what it's asking for "approximation"

#3 Will momentum be conserved while the pendulum is swinging? Explain.
-I said no because after collision, KE and PE are conserved but momentum is not conserved.
-I first thought it'd be because velocity is continuously lost while the pendulum reaches the top.
-I'm not sure what the correct reasoning would be.

#4 Since the velocity and therefore the momentum of the pendulum and ball are zero at the height h (this would be the max height), how can we say that momentum is conserved in the experiment?
-I'd say the momentum is conserved at the moment they are colliding but not for the entire experiment. Although there are external forces acting (which would bring the ball to stop at max height), just before and after the collision, the momentum of system would be nearly equal as long as the collision interaction is brief.

#5 Comment on the following statement: "The momentum of the paintball and bob could not be conserved in this experiment because of the large frictional forces between the bob and the entering paintball."
-If there's no momentum conserved, the bob would remain in its initial position since there's no momentum delivered from the paintball to the bob?

Even partial helps would be greatly appreciated!

## Answers and Replies

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ehild
Homework Helper
Hi Ariel, welcome to PF.

I'm doing the prelab questions which require conceptual questions, not so much of math.
The experiment is a typical ballistic pendulum lab - you'd shoot a paintball twoard a pendulum bob, and you measure the height the pendulum bob reaches after collision to calculate the related velocities.

## Homework Statement

#1 Define the paintball plus pendulum bob as a system at the instant that the paintball collides with the bob. Do any external forces act on this system?
#2 Will momentum be conserved during the collision? Is any approximation involved?
#3 Will momentum be conserved while the pendulum is swinging? Explain.
#4 Since the velocity and therefore the momentum of the pendulum and ball are zero at the height h (this would be the max height), how can we say that momentum is conserved in the experiment?
#5 Comment on the following statement: "The momentum of the paintball and bob could not be conserved in this experiment because of the large frictional forces between the bob and the entering paintball."

## Homework Equations

These questions are conceptual I think but relevant equations would be
Pi = Pf
m_ball * v_ball = (m_pend + m_ball) * v_pend

## The Attempt at a Solution

#1 Define the paintball plus pendulum bob as a system at the instant that the paintball collides with the bob. Do any external forces act on this system?
-I'm not so sure what it means by define them as a system...
-I said external forces would be gravity and air resistance (friction)
Consider the paintball and bob only. Gravity is an external force and there is some air resistance, too, but the force of the string the bob is attached to is also an external force for this system.

#2 Will momentum be conserved during the collision? Is any approximation involved?
-I said yes, conserved.
-I'm not sure what it's asking for "approximation"
Yes, we always assume that the momentum is conserved during a collision. Collision is a sudden event, happens in a very short time. Change of momentum is equal to impulse, FΔt. If the collision acts for such short time that FΔt is negligible, we can say that the momentum is conserved during the collision. Gravity is a constant force, but we can not say anything about the tension in the string during collision. But the tension is vertical at the moment of collision, the change of momentum is horizontal. The tension does not influence momentum change during the collision.
#3 Will momentum be conserved while the pendulum is swinging? Explain.
-I said no because after collision, KE and PE are conserved but momentum is not conserved.
-I first thought it'd be because velocity is continuously lost while the pendulum reaches the top.
-I'm not sure what the correct reasoning would be.
You are right, the momentum is not conserved while the bob is swinging. It is again "change of momentum = FΔt" If the time passes FΔt can not be ignored.
#4 Since the velocity and therefore the momentum of the pendulum and ball are zero at the height h (this would be the max height), how can we say that momentum is conserved in the experiment?
-I'd say the momentum is conserved at the moment they are colliding but not for the entire experiment. Although there are external forces acting (which would bring the ball to stop at max height), just before and after the collision, the momentum of system would be nearly equal as long as the collision interaction is brief.
Exact!
#5 Comment on the following statement: "The momentum of the paintball and bob could not be conserved in this experiment because of the large frictional forces between the bob and the entering paintball."
-If there's no momentum conserved, the bob would remain in its initial position since there's no momentum delivered from the paintball to the bob?
Think of the forces of interaction between the paintball and bob. The paintball exerts some force F on the bob and the bob exerts force -F on the paintball. The change of momentum of the bob is Δp(bob)=FΔt, the change of momentum of the paintball is Δp(paintball)=-FΔt. What is the net change of momentum of the system paintball + bob?

ehild

Thanks a lot!
Great help with great explanations :)
I'm going to use this forum very often from now!

ehild
Homework Helper
Thanks a lot!
Great help with great explanations :)
I'm going to use this forum very often from now!
I hope you will do

ehild