# Finding height dropped from Force vs. Time graph

In summary, a pumpkin was dropped from a balcony of a skyscraper and the data was collected. The pumpkin weighed 2.7kg and the impulse was 49.65Nm.

## Homework Statement

A pumpkin was dropped from a balcony of a skyscraper. The pumpkin happened to land on a sidewalk force sensor and the below data was collected. The pumpkin weighs 2.7kg.

a) From what height was the pumpkin dropped?

b) From what floor of the skyscraper was the pumpkin probably dropped?

## Homework Equations

Potential Before = Kinetic After: mgh = (1/2)mv^2

Solving for v gives: v = sqrt(2gh)

a = F/m

Vf = a*t+Vi
Sf = .5*at^2+Vi*t+ Si

## The Attempt at a Solution

First I used mgh = .5mv^2 and solved for v.

This gave me v = sqrt(2gh)

I figure that finding the area under the curve of the graph gives the total force on the pumpkin as it is hitting the ground. I haven't done this yet, but I am not too worried about getting an exact answer for this part. I more want to make sure I know how to solve the rest of the problem.

I tried using kinematic equations to solve for height, but I ended up with h being 0, so I think I am not using the right concept and/or equation here.

We are currently studying conservation of momentum, but I don't see how that is helpful here for determining the height the object was initially dropped from.

Hopefully I am missing something obvious?

Last edited:
Hello. Welcome to PF!

The area under the graph does not give you the "total force". It gives you something called "impulse". Review your notes or textbook for information about impulse and how it is related to momentum.

TSny said:
Hello. Welcome to PF!

The area under the graph does not give you the "total force". It gives you something called "impulse". Review your notes or textbook for information about impulse and how it is related to momentum.

Right, I was mistaken. I think I've got it now.

The impulse is equal to the change in momentum over that time period.

Change in momentum = area under the curve = impulse = J

So, using that I solved change in momentum:

2.7(v) - 2.7(0)
2.7v = J
v = J/2.7

I estimated J by using Reimann Sum, got 49.72.

Then I just used conservation of energy, mgh = .5*m*v^2 and got 17.29 meters for h.

Hopefully this is right, I think I didn't quite understand impulse.

I estimated J by using Reimann Sum, got 49.72.

Then I just used conservation of energy, mgh = .5*m*v^2 and got 17.29 meters for h.
I got J = 49.65 Nm and h = 17.24 m.
I'm not sure what floor that was from, but when thinking "skyscraper", it was not very high.
Once again, a problem with more drama and suspense needed. :)

TomHart said:
I got J = 49.65 Nm and h = 17.24 m.
I'm not sure what floor that was from, but when thinking "skyscraper", it was not very high.
Once again, a problem with more drama and suspense needed. :)

Thanks, I'm glad I was close!

## What is a Force vs. Time graph?

A Force vs. Time graph is a visual representation of the relationship between the force applied to an object and the time it takes for that force to act on the object. The force is typically plotted on the y-axis and time on the x-axis.

## How can I find the height dropped from a Force vs. Time graph?

To find the height dropped from a Force vs. Time graph, you will need to calculate the area under the curve. This can be done by dividing the graph into smaller, equal sections and calculating the area of each section. Then, add all of the areas together to find the total area under the curve. This value represents the height dropped.

## What units are used in a Force vs. Time graph?

The units used in a Force vs. Time graph will depend on the specific force and time measurements being used. However, the most common units for force are Newtons (N) and for time are seconds (s).

## What variables affect the height dropped in a Force vs. Time graph?

The height dropped in a Force vs. Time graph can be affected by several variables, including the initial force applied, the mass of the object being dropped, and the resistance of the medium the object is falling through (such as air or water).

## Can a Force vs. Time graph be used to find the height dropped for any object?

No, a Force vs. Time graph can only be used to find the height dropped for objects that experience a constant force while falling. If the force changes or is not constant, the graph cannot accurately determine the height dropped.

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