Interactive Lecture Demonstration 19 – Ballistic Pendulum

 

 

 

In this demonstration, a bowling ball and a sandbag hang side by side. Both objects can swing like pendulums. The sandbag will be drawn back so that it is a height hi above the bowling ball, and will then be allowed to swing to hit the bowling ball. Both objects will then swing together to some final height hf . The bowling ball is a ballistic pendulum, a device that is often used to measure the speeds of bullets by measuring the height to which the pendulum swings when hit by a bullet. Here, we will use the ballistic pendulum to determine what the speed of the sandbag was just before it hit the bowling ball. We will then compare our answer with the speed predicted using conservation of energy for the sandbag as it swings downward.

 

The bowling ball weighs 11 pounds. The sandbag weighs 16 pounds.

 

 

 

 

 

 

 

 

 

 

 

 

 

Part 1: Setting Up the Problem

 

  1. Watch the demonstration, and record the heights hi and hf .
  2. We want to find the speed of the sandbag just before it hit the bowling ball by working backwards from the measured final height of the two objects. We might want to use conservation of energy or conservation of momentum here. Before using either conservation law, though, we should decide whether energy or momentum is actually conserved in this problem. Whether energy or momentum is conserved depends on several things: a) what we choose our system to be, b) what we choose to be the "initial" and "final" locations for our system, and c) what forces act on our system (and whether those forces make an impulse or do work on the system).

 

We hope you realize that it is important to choose the system to include both the bowling ball and the sandbag, if there is any hope of applying the laws of conservation of energy or momentum here.

 

Once we choose the system, though, we still must choose appropriate initial and final locations. There are three possible choices here. For each of those choices, decide whether it would be valid to apply the laws of conservation of energy and momentum. Whatever you decide, be sure to give the reasons for your answers.

 

Initial and Final Locations

Energy Conserved ? (Y/N)

Reason

Momentum Conserved ? (Y/N)

Reason

i = just before bag hits ball

f = ball and bag are at max height

 

 

 

 

i = just after bag hits ball

f = ball and bag are at max height

 

 

 

 

i = just before bag hits ball

f = just after bag hits ball

 

 

 

 

 

 

Part 2: The Upswing

 

Apply the law of conservation of energy to find the speed of the combined bowling ball/sandbag system (they are moving together and thus have the same speed) just after they collided. Yes, you need a force diagram.

 

 

 

 

 

 

 

 

 

Part 3: The Collision

 

Apply the law of conservation of momentum to find the speed of the sandbag just before it hit the bowling ball. You will need a force diagram here, too.

 

 

 

 

 

 

 

Part 4: The Downswing

 

Now that you have determined the speed of the sandbag before it hit the bowling ball, compare your answer with the speed you predict based on knowing the initial height of the sandbag. Yes, you need another force diagram.