## Jump Launch Velocity from Impulse

### Materials:

- lab sheet and writing utensil
- calculator
- spreadsheet and graphing software
- for distance learners, access to online forums, videos, and help features for the spreadsheet software will likely be necessary
- tape
- Digital Force PlateĀ + computer with sensor control and analysis software
- Camera with slow-motion capability

### Data Acquisition

Place a piece of tape on the jumper’s center of mass so that you can use a camera with slow-motion capability to record the change in height of the their center of mass during the jump. You may need to look up some information on where to locate your center of mass. Cite your sources here:

We will use a force plate to measure the normal force applied to the jumper’s feet. Have the jumper stand on the force plate and push the zero button. Now the force plate will read the difference between the normal force and their weight, which is the net force acting on them. It should be zero when they are at rest.

Have the jumper practice jumping and landing on the force plate while trying to keep their arms in the same position during the jump so that the location of their center of mass doesn’t change much throughout the jump.

Now record the height of the center of mass throughout a jump and landing while recording the normal force on the person.

Record the change in height here, we will use that later:__________. Keep your video recording for later use as well.

### Applying Impulse-Momentum to the Entire Jump

What was change in momentum for the person over the entire jump, from starting at rest, through launch phase, air phase, landing phase, and finishing at rest.

Based on your answer above and the impulse-momentum theorem, what should the total impulse on the person have been for the overall jump?

Based on your previous answer what should the average force on the person be for the entire jump?

Use the lab software to calculate the calculate the average force applied to the person throughout the entire jump. Does the result agree with your answer? Explain.

### Applying Impulse-Momentum During Launch Phase

Use the force data to calculate the average force applied to the person from the start of their jumping movement until they leave the platform. Record here:

Also record the peak force during this launch phase of the jump (for later use):

Record the time interval used in this average. (The time over which the launch phase lasted.)

Calculate the impulse applied to the person during the launch phase of the jump.

According to the impulse-momentum theorem, what change in momentum should the person experience during the launch phase?

Their initial momentum was zero, so what should the their final momentum be at the end of launch phase?

### Applying Impulse-Momentum During Air Phase

The only force acting on the person during the air phase is gravity. You already know the size of that force (it’s their weight as measured by the force plate). Use the impulse-momentum theorem to calculate how long it will take the gravitational force to change their momentum from the initial launch value to zero.

The momentum of the jumper is zero at the very top of the jump, so the time you found is half of the total hang time.

Based on your answer above, what will the hang time be?

Does that answer agree with the hang time recorded by your force plate? Explain, including values from your data.

### Calculating Launch Velocity

Based on the level of agreement between expected and observed hang time, do you think that using the impulse-momentum theorem to analyze the jump is reasonable? Explain.

Use your previous result for the launch momentum, along with the definition of momentum, to calculate the velocity of the person as they left the platform at the end of the launch phase.