A 48.0 kg diver steps off a 10.0 m high diving board and drops straight down into the water. If the diver comes to rest 5.0 m below the surface of the water, determine the average resistance force exerted on the diver by the water.
N
Gravity continues to work on the diver as he descends under water. This mst be taken into account.
The total potential energy (P.E) loss of the diver at greatest depth is M g (10 + 5) = 7056 J
Work done by the water on the diver, or of the diver upon the water, is equal to that P.E. loss at the greatest depth.
Thus 7056 J = F*5m
where F is the average force (averaged over distance, not time).
F = 1411 N
Don't know the answer but posted it on the Diving News Facebook page: diving News - By flipnrip
Roughly twice the gravitational acceleration of 9.8 to stop in have the time. Given F=MA then F = 48*19.6 or about 950 (kg*m/(S^2)).
SOmeone helped on the facebook page: diving news by flipnripcom
353.16lb of resistance to stop at 5M (that is for the distance of their feet hitting to 5M of their feet depth). m*g*(10+5) = F*5
F = 3*m*g = 1412N = 353.16lb
...A far better calculation uses the drag equation: Fd=0.5*rho*A*Cd*v^2
You can find the force at each point through the water instead of just the average. However, it is difficult to say how accurate it is-would need a little video analysis to justify it. I will put up a note with the complete analysis when I get a chance.
To determine the average resistance force exerted on the diver by the water, we need to use the concept of work and energy.
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done on the diver by the water is equal to the change in the gravitational potential energy of the diver.
First, let's calculate the initial potential energy of the diver on the diving board. Potential energy is given by the formula:
Potential energy = mass x gravitational acceleration x height
In this case, the mass of the diver is 48.0 kg, the gravitational acceleration is 9.8 m/s^2, and the height is 10.0 m. Plugging these values into the formula, we get:
Potential energy = 48.0 kg x 9.8 m/s^2 x 10.0 m = 4,704 J
Next, let's calculate the final potential energy of the diver when they come to rest 5.0 m below the surface of the water. Using the same formula, we get:
Potential energy = 48.0 kg x 9.8 m/s^2 x 5.0 m = 2,352 J
Now, the work done by the water is equal to the change in potential energy, which is given by the difference between the initial potential energy and the final potential energy:
Work done by water = Initial potential energy - Final potential energy
= 4,704 J - 2,352 J
= 2,352 J
Since work is equal to force multiplied by displacement, we can calculate the force exerted by the water using the formula:
Force = Work / Displacement
In this case, the work done by the water is 2,352 J and the displacement is 5.0 m. Plugging these values into the formula, we get:
Force = 2,352 J / 5.0 m = 470.4 N
Therefore, the average resistance force exerted on the diver by the water is 470.4 N.