# How High Does the Force Platform Indicate the Athlete Jumped?

• szimmy
In summary, The "force platform" is a tool used to analyze athlete performance through measuring vertical force as a function of time. The vertical divisions of the graph represent 0.65 kN and the horizontal divisions represent 0.50 s. From the graph, it can be determined that the impulse of the athlete is 650N. To find the height of the jump, the equation h = (650/m)^2/2g can be used, but without knowing the mass, a numerical value cannot be determined. Calculus is not necessary to solve this problem, but the area under the curve can be approximated by "counting squares" or assembling geometric shapes.
szimmy

## Homework Statement

The "force platform" is a tool that is used to analyze the performance of athletes by measuring the vertical force as a function of time that the athlete exerts on the ground in performing various activities. A simplified force vs. time graph for an athlete performing a standing high jump is shown in Figure P6.66. The vertical divisions of the graph represent 0.65 kN and the horizontal divisions represent 0.50 s. The athlete started the jump at t = 0.0 s. How high did this athlete jump?
Picture of graph: http://www.webassign.net/sercp/p6-66alt.gif

## Homework Equations

J = FΔt
J = ΔP
J = m(vf - vi)
FΔt = mvf (since the jump starts from rest)

## The Attempt at a Solution

From the graph I was able to get that the impulse is 650N. The problem is I have no idea how to use this to get the height he jumped, I feel like I need a mass to solve this.
Given that J = m(vf - vi)
This means that FΔt / m = vf (vi is 0 because starting from rest)
This vf would be the vi for the jump, so mgh = 1/2 m v^2
h = v^2/2g
h = (650/m)^2/2g
h = 422500 / 2*g*m^2
I'm stuck from here, none of my classmates could figure it out either. If somebody could give me a push in the right direction I would appreciate it. I feel like the solution is obvious and I'm just thinking too hard.

Last edited:
szimmy said:
From the graph I was able to get that the impulse is 650N. The problem is I have no idea how to use this to get the height he jumped, I feel like I need a mass to solve this.
What value does the graph show for time ##t \le 0##? Why do you suppose that is?

gneill said:
What value does the graph show for time ##t \le 0##? Why do you suppose that is?

Wow, I can't believe I didn't realize that before. He's standing still so the 650N when he's standing still is mg. Thanks for your help!

Disregard this post. I asked a question and then went and tinkered with some stuff and (somehow) made it work. I couldn't find a way to delete the post so I'm just editing it.

Last edited:
szimmy said:
I just have one more question. Our school doesn't offer calculus based physics (I'm in AP Physics B, but also calc) so we aren't required to do calculus to solve any problems. This normally isn't a problem, but the F versus T graph is a curve is it not? Is it possible for me to find the area under the curve to find the impulse without using calculus? This has me confused now.

Well, since you aren't given an equation for the curve, calculus isn't going to be much help anyways. You're left with "counting squares" or assembling a number of geometric shapes to cover the area to reach an approximation.

## 1. What is impulse?

Impulse is the change in momentum of an object. It is a vector quantity that is equal to the force applied to the object multiplied by the time interval over which the force is applied.

## 2. How is impulse related to energy?

Impulse is closely related to energy, as both are measures of the motion of an object. Impulse is the change in momentum, while energy is the ability to do work. In some cases, impulse can lead to a change in an object's kinetic or potential energy.

## 3. What is the difference between elastic and inelastic collisions?

In an elastic collision, both kinetic energy and momentum are conserved. This means that the objects involved bounce off each other without any loss of energy. In an inelastic collision, some of the kinetic energy is converted into other forms, such as heat or sound, and the objects may stick together after colliding.

## 4. Can impulse be negative?

Yes, impulse can be negative. This occurs when the force applied to an object is in the opposite direction of its initial motion. In this case, the impulse will result in a decrease in the object's momentum.

## 5. How is impulse calculated?

Impulse can be calculated using the equation J = FΔt, where J is impulse, F is the force applied, and Δt is the time interval over which the force is applied. Alternatively, impulse can also be calculated by finding the area under a force vs. time graph.

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