What is the average force exerted on a falling diver?

In summary, to find the magnitude of the average force exerted on a 74.0 kg diver falling from a height of 4.50 m into a swimming pool and stopping in 1.58 s, the kinematics equation Vf^2 = Vi^2 + 2ad can be used to find the final velocity of 9.396 m/s. This can then be used to calculate the momentum of the diver, which is 695.3 kg*m/s. Dividing this by the time of 1.58 s gives an average total force of 440.1 N upwards. To find just the average force of the water on the diver, this value would need to be divided by 2.
  • #1
BuBbLeS01
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0

Homework Statement


A 74.0 kg diver falls from rest into a swimming pool from a height of 4.50 m. It takes 1.58 s for the diver to stop after entering the water. Find the magnitude of the average force exerted on the diver during that time.


Homework Equations


Favg = J/change in T
J = 1/2 * Base * Height


The Attempt at a Solution


So the base = 1.58s
How do we calculate the Height (Fmax)?
 
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  • #2
I guess J also equals the change in P (which I don't understand since I thought it was the area under the curve). Is that the right equation for J??
 
  • #3
BuBbLeS01 said:

Homework Equations


Favg = J/change in T
This makes sense. It describes average force in terms of impulse and time.
J = 1/2 * Base * Height
Huh? Where does this equation come from?

J = impulse = change in momentum.

What's the diver's change in momentum? Hint: What's his initial momentum as he just hits the water?
 
  • #4
I thought J was equal to the area under the curve (which is usually triangular shape).
Pi = 74kg * 0m/s
Pf = 74kg * (4.5m/158s)
 
  • #5
BuBbLeS01 said:
I thought J was equal to the area under the curve (which is usually triangular shape).
I suppose J would equal the area of a Force vs. Time curve. But are you given any such curve in this problem? No.

No need for any curves, just find the speed of the diver as he hits the water and use that to find his momentum.
 
  • #6
To find the speed I just did Distance/Time so I got 4.5m/1.58s = 2.85m/s
J = Pf-Pi
Pf = Pi
(74kg*2.85m/s) - (74kg*0m/s) = 25.96kg*m/s
Favg = J/T = 25.96/1.58s = 16.43N*s
 
  • #7
BuBbLeS01 said:
To find the speed I just did Distance/Time so I got 4.5m/1.58s = 2.85m/s
That time is the time it takes him to stop once he hits the water. It's got nothing to do with the time he takes to fall the 4.5 m. (Also, realize that the speed is not constant as he falls.) You need a little kinematics to figure out the speed. (Or you can use energy methods, if that's easier for you.)
 
  • #8
What kinematics equation do I use? They all have acceleration in them, so do I just use 9.8m/s^2? I thought that was an external force and we didn't include it?
Vf = Vi +at
Can I use that one?
 
  • #9
Yes, the acceleration during the dive will be 9.8 m/s^2. But, since you don't have the time, that equation isn't good enough. Find one that relates velocity to acceleration and distance.
 
  • #10
Vf^2 = Vi^2 + 2ad
 
  • #11
I get a final velocity of 9.396m/s
 
  • #12
BuBbLeS01 said:
I get a final velocity of 9.396m/s
Good! Use that to find the momentum.
 
  • #13
(74kg*9.396m/s) - (74kg*0m/s) = 695.3kg*m/s
Then...
Favg = J/T = 695.3/1.58 = 440.1 N*s
 
  • #14
Good. That's the average total force on the diver: 440.1 N upwards. That includes both gravity and the force of the water. If they wanted just the average force of the water on the person, what would that be?
 
  • #15
Ummm...divide by 2? I don't know? Or divide by g?
 

What is the force on a falling diver?

The force on a falling diver is a combination of two forces: the force of gravity pulling the diver towards the ground, and the force of air resistance pushing against the diver as they fall through the air. These forces together make up the net force acting on the diver.

How does the force of gravity affect a falling diver?

The force of gravity is what causes the diver to accelerate towards the ground. As the diver falls, their speed increases due to the constant pull of gravity. This acceleration will continue until the diver reaches terminal velocity, when the force of air resistance is equal to the force of gravity.

What is terminal velocity?

Terminal velocity is the maximum speed that a falling object can reach due to the balance between the force of gravity and the force of air resistance. For a diver, this is typically around 120 miles per hour, but can vary based on their size, shape, and position in the air.

How does air resistance affect a falling diver?

Air resistance is the force that opposes the motion of an object through the air. As a diver falls, they encounter more and more air molecules, causing air resistance to increase. This force eventually becomes equal to the force of gravity, resulting in a constant velocity known as terminal velocity.

What factors can affect the force on a falling diver?

The force on a falling diver can be affected by several factors, including the mass, size, and shape of the diver, as well as their position in the air. The density and viscosity of the air can also play a role in the force of air resistance. Additionally, external factors such as wind or air currents can also impact the force on a falling diver.

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