Interactive Lecture Demonstration 12 – Kinetic and Gravitational Energy

In this demonstration, a ball will roll down a curved ramp that sits on a tabletop. The ball will start from rest and will be moving horizontally when it gets to the bottom of the ramp. Once the ball leaves the ramp, it will undergo projectile motion until it hits the ground.

The purpose of this activity is to test the law of conservation of energy for the ball. The ball will have gravitational energy, but no kinetic energy, at the top of the ramp. It will have lost gravitational energy and gained kinetic energy when it gets to the bottom of the ramp. Using the law of conservation of energy, we can predict how fast the ball will be traveling at the bottom of the ramp – we will call that the "launch speed." We will test our prediction by measuring the ball's horizontal displacement between leaving the ramp and hitting the floor, and comparing the measured displacement with the value calculated using the predicted launch speed and equations of motion for projectiles.

1. The center of mass of the ball at the top of the ramp is 13 cm higher than at the bottom of the ramp. Predict the ball's speed when it reaches the bottom, assuming that the ball begins at rest. Note that this problem is impossible for us to solve using Newton's Laws, since the force of the curving track on the ball is constantly changing as the balls rolls down the ramp. You will need to use conservation of energy. Be sure to give the reason that the ball's energy is conserved.

2. Now use your result from #1 to predict the ball's horizontal displacement between leaving the ramp and hitting the ground. This is a DVAT problem in two dimensions – what will be your 5 known variables ? (you may use a meter stick to measure any distances you need)

3. Now we'll test your prediction. The ball will leave a mark on a sheet of paper placed near the spot where we think the ball will hit the floor, and we will measure the horizontal displacement form the bottom of the ramp. How close was your prediction ?

4. Suppose the ball rolled down a differently-shaped ramp that starts and ends at the same heights that the first ramp did. How would your calculated launch speed change ?

5. One more conservation of energy problem: calculate the ball's speed just before it hits the ground.

6. Note that we could also calculate the speed just before hitting the ground using DVAT formulas and making a velocity triangle, although it is easier in this case to use conservation of energy. For practice, calculate the speed using DVAT methods and verify that your answer is the same as the one you get using conservation of energy.

7. Could you calculate the direction of the ball's velocity just before hitting the ground using conservation of energy ? Using DVAT's ?