Is This Scenario an Example of an Elastic Collision?

[Nicholson]

Homework Statement

This is actually a lab-
A ball projectile is fired from a spring gun into a free-hanging pendulum, the pendulum catches the ball and travels a certain vertical measurement.
#1-Is this an elastic equation
#2-Calculate the kinetic energy the instant before and the instant after the collision.

Homework Equations

K=1/2m*v^2
m=0.0669kg
v=6.535 m/s

The Attempt at a Solution

#1- I think that this is an elastic equation because no energy is lost in the collision- it is transferred from the spring gun to the pendulum (discounting air resistance).

#2- I calculated the kinetic energy using the above equation to be 1.43 J- I am thinking that this is the kinetic energy before the collision and it is -1.43 after?

If I'm wrong I would really appreciate being pointed in the right direction.

 

[collinsmark]

Hello Nicholson,

Welcome to Physics Forums!

#1- I think that this is an elastic equation because no energy is lost in the collision- it is transferred from the spring gun to the pendulum (discounting air resistance).

The problem statement says that "the pendulum catches the ball." Is there any energy (such as thermal energy) involved in the act of something catching the ball?

(Hint: If you drop a physics textbook on the floor, and it doesn't bounce back up to its original position [but rather just stays on the floor], you can think of this process as the floor "catching" the book. Where does the book's kinetic energy go? Is this process an elastic collision? [If you answer 'yes', what would you consider to be an inelastic collision?] )

#2- I calculated the kinetic energy using the above equation to be 1.43 J- I am thinking that this is the kinetic energy before the collision and it is -1.43 after?

Something isn't quite right. Your kinetic energy before the collision is right assuming that v is the speed of the ball just before the collision, and m is the mass of the ball. You'll have to show your work though if you want more detailed help. What is the height of pendulum's vertical measurement? is m the mass of the ball or the mass of the pendulum bob? What is the mass of the other object? How did you obtain v? Was it directly measured or did you calculate it from somewhere else?

 

[Nicholson]

#1- I am assuming that during the collision the momentum of the system is conserved- however, the more I think about it kinetic energy has to be lost from the point at which the projectile is released from the spring... making it an inelastic collision.

#2- The mass and velocity were calculated in the lab and I know for a fact that they are correct. Think I figured out where I went wrong-
To answer the question I calculated the velocity after the collision and the combined mass of the pendulum and projectile:
m=0.3458 kg
v= 1.32076 m/s
and using k=1/2m*v^2 calculated 0.301 J for the kinetic energy after the collision- confirming that it is and inelastic collision

 

[collinsmark]

#1- I am assuming that during the collision the momentum of the system is conserved-

That's good. Momentum is always conserved. (Assuming everything in the system is accounted for [and is a lot easier to account if ignoring friction.])

however, the more I think about it kinetic energy has to be lost from the point at which the projectile is released from the spring... making it an inelastic collision.

Well, yes. But I'd like to make sure you have the reasons right.

Sure, there might be some kinetic energy lost due to air resistance, etc., between the time the ball is released from the spring to the time immediately before the ball reaches the pendulum. But that is not at issue here, since it doesn't involve the collision itself. Any particular loss of kinetic energy that happens decidedly before the collision has no bearing on whether the collision itself is elastic or not.

We need to consider only the collision itself. And here is a big hint: Any time there is a perfectly elastic collision between two objects, the two objects will bounce off each other. So do the ball and the pendulum bob bounce off each other or do they stick together?

#2- The mass and velocity were calculated in the lab and I know for a fact that they are correct. Think I figured out where I went wrong-
To answer the question I calculated the velocity after the collision and the combined mass of the pendulum and projectile:
m=0.3458 kg
v= 1.32076 m/s
and using k=1/2m*v^2 calculated 0.301 J for the kinetic energy after the collision- confirming that it is and inelastic collision

Very nice. It is an inelastic collision.

 

[paranormal]

I would like to confirm that your understanding is correct. This is indeed an elastic equation because in an elastic collision, the total kinetic energy of the system is conserved. In this case, the kinetic energy is transferred from the spring gun to the pendulum without any loss, as you mentioned.

In terms of calculating the kinetic energy before and after the collision, your calculation is correct. The kinetic energy before the collision is 1.43 J and after the collision, it is still 1.43 J. This is because the total kinetic energy of the system is conserved in an elastic collision. However, it is important to note that the velocity of the pendulum and the ball may change after the collision, but the total kinetic energy will remain the same.

I would also recommend double-checking your calculations and units to ensure accuracy. Overall, your understanding and approach to this problem are correct. Great job!