What is the average force exerted on a falling diver?

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Homework Help Overview

The problem involves a diver falling from a height of 4.50 m into a swimming pool and the average force exerted on the diver during the deceleration phase after entering the water. The subject area includes concepts from mechanics, specifically impulse, momentum, and kinematics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between impulse and momentum, questioning the equations used to calculate average force and the change in momentum. There are attempts to clarify the definitions and applications of impulse, as well as the kinematic equations relevant to the diver's fall.

Discussion Status

The discussion is active with participants exploring different interpretations of impulse and momentum. Some have provided calculations for the diver's final velocity and momentum, while others are questioning the assumptions regarding acceleration and the equations to use. There is no explicit consensus on the average force of the water on the diver.

Contextual Notes

Participants note the importance of distinguishing between the time taken to fall and the time taken to stop in the water. There is also mention of the gravitational force acting on the diver and its implications for the calculations.

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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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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??
 
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?
 
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)
 
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.
 
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
 
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.)
 
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?
 
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?
 

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