# University of Wisconsin Green Bay

You are helping your friend prepare for the next skateboard exhibition by determining if the planned program will work. Your friend will take a running start and then jump onto a heavy-duty 15-lb stationary skateboard. The skateboard will glide in a straight line along a short, level section of track, then up a sloped concrete wall. The goal is to reach a height of at least 10 feet above the starting point before coming back down the slope. Your friend's maximum running speed to safely jump on the skateboard is 23 feet/second. Your friend weighs 150 lbs.
This problem was used with permission of Dr. Ken Heller of the University of Minnesota Physics Education Research Group.

• In this problem, you are asked to find the height to which your friend rises when he or she jumps on a skateboard with a running start. Any time you are asked to relate speed and position of an object, you should check to see if you can use Conservation of Energy to solve the problem. In this case, you have an unknown amount of force that takes energy out of the system when your friend collides with the skateboard and so you cannot track non-conservative work during the collision. So this is not a one-step problem.

However, the unknown energy loss occurs during a collision. Any time you are asked to find speed or velocity of an object just before or just after a collision or separation, you can likely use Conservation of Momentum to solve that part of the problem.

This, then, is a two part problem. Momentum is conserved as your friend collides with the skateboard, and energy can be tracked as the skateboard goes up the incline. If you do not recognize both parts of the problem before you begin, that is fine. You can start the problem with either momentum or energy and will quickly find that you need to do an additional analysis to complete the problem

• For Conservation of Momentum problems, you always draw a picture of the system immediately before the collision or separation and another picture immediately after (Points 1 and 2.) Because momentum depends on mass and velocity, label all mass and velocity information on the pictures. This helps to avoid mistakes as you fill into the equation later.

For Conservation of Energy questions, you want to show the velocity and position information at all points over which you track energy (Points 2 and 3.)

• Any time you understand the motion of a system for which Fextermal Δt is about 0, you can usethe Conservation of Momentum equation. Practically, this means that any time you want to explore what happens during a collision or explosion you will consider Conservation of Momentum.

Any time you understand the motion of an object by looking at its energy, you begin with the Conservation of Energy equation. This form of the equation works whenever you can track Wnc.

In this problem, we know information about Point 1 and want to learn about Point 3. Therefore, we will begin with the Conservation of Momentum equation--we can use information about Point 2 to learn about Point 2. From their, energy at Point 2 can be tracked to learn about Point 1.

• After your friend lands on the skateboard, they move together with a speed of 21 m/s. Scroll down to find the maximum height to which they can rise up the ramp.

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Step 2

If your friend jumps on the skateboard from a running start at 23 ft/s, he or she will only rise up the ramp about 7 feet, falling short of the desired 10 feet for the program.

• Although this problem asked you to find the height your friend could move up a ramp given an initial running speed, you are not able to compare energy at the start and the end of the problem because an unknown amount of energy is lost from the system as your friend lands on the skateboard. The energy chain for this part of the motion is

kinetic energy of your friend --> kinetic energy of your friend and the skateboard + heat/sound

You can, however, compare momentum during the collision because no external force (in this case friction, normal force on the skateboard, gravity) does significant amount of work on the system during the time of the collision.

Following the collision, the energy chain is

kinetic energy of your friend and the skateboard --> gravitational potential energy of your friend and the skateboard

and so energy can be tracked for that portion of the motion.

Note that a height of 6.9 feet is reasonable and makes sense as the solution to this problem.