Force/Energy Problem: Jump from Window

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In summary, a man weighing 75kg jumps from a window 1.0m above the side walk. His speed just before his feet strike the pavement is 4.43 m/s. If the man jumps with his knees and ankles locked and the only cushion for his fall is approximately 0.50 cm in the pads of his feet, the average force exerted on him by the ground is to be calculated using Newton's second law. This involves finding the constant acceleration needed for this and then relating it to the force.
  • #1
arizona_cards_11
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Question

A 75kg man jumpst from a window 1.0m above the side walk.

a) What is his speed just before his feet strike the pavement?

b) If the man jumps with his knees and ankles locked, the only cushion for his fall is approximately 0.50 cm in the pads of his feet. Calculate the average force exerted on him by the ground in this situation.

Work

a) MEi = MEf

PEi + KEi = PEf + KEf ===> mgh + (.5)mv^2 = mgh + (.5)mv^2

After plugging in values:

736 + 0 = 0 + 37.5v^2 ===> V^2 = 19.6 ===> V = 4.43 m/s

b) I'm not sure how to approach this problem. I assume I'm basically trying to find the normal force of the man...but I don't know what the height really has to do with the problem unless I'm supposed to use energies to relate to the force in some way.
 
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  • #2
You are given the initial velocity from the previous question, and the distance of acceleration by the thickness of his foodpads. I suppose they want you to calculate the constant acceleration needed for this, and then relate that to the force using Newtons second law.

- Kerbox
 
  • #3


To calculate the average force exerted on the man by the ground, we can use Newton's second law, which states that force equals mass times acceleration (F=ma). In this case, we know the mass of the man (75kg) and the acceleration due to gravity (9.8 m/s^2). However, we need to calculate the deceleration the man experiences when his feet hit the ground. We can do this by using the equation v^2 = u^2 + 2as, where u is initial velocity (4.43 m/s, calculated in part a), a is acceleration (-9.8 m/s^2) and s is the distance the man's feet travel before coming to a stop (0.005 m).

Plugging in values and solving for a, we get a = -2029.4 m/s^2. This is the deceleration the man experiences when his feet hit the ground. Now, we can calculate the average force using F=ma.

F = (75kg)(-2029.4 m/s^2) = -152205 N

Note that the force is negative because it is acting in the opposite direction of the man's initial velocity. This means that the man experiences a very large force (152205 N) when his feet hit the ground, which could result in serious injury. It is important for individuals to properly bend their knees and absorb the impact of a fall to reduce the force exerted on their body.
 

1. What is the force required to jump from a window?

The force required to jump from a window varies depending on factors such as the height of the window, the weight and strength of the individual, and the surface they are jumping onto. It is not recommended to intentionally jump from a window as it can be dangerous and potentially result in serious injury.

2. How does the height of the window affect the force needed to jump?

The higher the window, the more force is required to jump from it. This is because the individual has to overcome the force of gravity and the potential energy stored in their body as they fall. Additionally, the impact force upon landing also increases with height, making it more dangerous.

3. Is there a specific technique to jump from a window safely?

There is no specific technique to jump from a window safely. The safest option is to avoid jumping from a window altogether. If it is absolutely necessary, the individual should try to land on a soft surface and try to roll or distribute the impact force as evenly as possible.

4. How does the weight of the individual affect the force needed to jump from a window?

The weight of the individual does not have a direct impact on the force needed to jump from a window. However, a heavier individual may experience a higher impact force upon landing due to their greater mass.

5. Can jumping from a window result in potential energy being converted into kinetic energy?

Yes, jumping from a window involves a conversion of potential energy stored in the individual's body into kinetic energy as they fall. This kinetic energy can then be converted into impact force upon landing, potentially causing injury.

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