# Calculating Impact Force of Man Falling onto Cushion

• eureka_beyond
In summary: The problem is that he's calculating the impact force (the force of the cushion on the man) rather than one of the other forces acting on him.
eureka_beyond

## Homework Statement

the question goes like this
a man of mass 70kg falls onto a rescue cushion from a height of 7 m he comes to rest 0.2s after he reaches the cushion the cushion is 2m high when inflated
a)find the impact force acting on him (take the weight of the man into account)
b)by how many times is the impact force greater than his weight?

## The Attempt at a Solution

a) For a, I first calculated the change of momentum of the man, which is 700kgms-1, then the impact force will be the change of momentum over time, which gives an answer of 3500N, which is a wrong answers since the answer in the book is 4200, I don't get it...

eureka_beyond said:
then the impact force will be the change of momentum over time,
No, the change in momentum over time gives the net force on the man. The impact force (the force of the cushion on the man) is only one of the forces acting on him. What's the other?

Your calculation for the change in momentum is wrong. Or rather, the answer you give is wrong. How did u calculate this?

It seems you have taken the change of momentum as his weight. That is, multiplied his mass 70kg with gravity ~10. However this is NOT the change in momentum.

You need to consider the change in his potential energy to calculate his velocity.

You first need to find the velocity (V)of the man just before he strikes the cushion.
(Use the familiar equations of motion for falling through a height of 7m onto cushion 2m thick with acceleration due to gravity.)
Use this velocity, combined with his mass to find his momentum just before he strikes the cushion.
Then use your impulse formula to find the impact force. (eta. noting the point in the question about his weight)

Last edited:
H_man said:
Your calculation for the change in momentum is wrong. Or rather, the answer you give is wrong. How did u calculate this?

It seems you have taken the change of momentum as his weight. That is, multiplied his mass 70kg with gravity ~10. However this is NOT the change in momentum.

You need to consider the change in his potential energy to calculate his velocity.
FYI: There's nothing wrong with the OP's calculation for the change in momentum. That's not the problem.

## 1. How do you calculate the impact force of a man falling onto a cushion?

The impact force can be calculated using the formula F = m x a, where F is the force, m is the mass of the person, and a is the acceleration due to gravity (9.8 m/s²). To determine the mass of the person, you can use a scale or measure their weight and convert it to kilograms.

## 2. What factors affect the impact force of a man falling onto a cushion?

The impact force can be affected by several factors such as the height from which the person falls, their weight or mass, the type of cushion or surface they are falling onto, and the angle at which they hit the cushion. Air resistance and the person's body position during the fall can also impact the force.

## 3. How does the type of cushion affect the impact force?

The type of cushion can affect the impact force as some materials are better at absorbing impact energy than others. A softer and more compressible cushion, such as a foam or gel cushion, will absorb more of the force and reduce the impact on the person. A harder cushion, such as a wooden or metal surface, will not absorb as much force and can result in a higher impact force.

## 4. Is there a way to reduce the impact force of a person falling onto a cushion?

Yes, there are a few ways to reduce the impact force. One way is to increase the surface area of the cushion by using a larger or thicker cushion. This will distribute the force over a larger area, reducing the impact on a specific point. Another way is to use cushions made of materials that are designed to absorb impact energy, such as memory foam or air cushions. Additionally, having the person land on the cushion at an angle rather than straight on can also help reduce the impact force.

## 5. What are some real-world applications of calculating the impact force of a person falling onto a cushion?

Calculating the impact force of a person falling onto a cushion can be useful in various industries, such as sports, automotive, and safety. In sports, understanding the impact force can help design better protective gear for athletes, and in automotive, it can aid in designing safer cars and car seats. In safety, this calculation can be applied to determine the force of a person falling from a height onto a safety mat or landing pad.

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