Problem of conservative and non-conservative forces

[dmatador]

A 65.1 kg person jumps from rest off a 3.04 m-high tower straight down into the water. Neglect air resistance during the descent. She comes to rest 1.11 m under the surface of the water. Determine the magnitude of the average force that the water exerts on the diver. This force is nonconservative.

I've tried to solve the first part using that fact that the initial energy and the final one right before entering the water will be equal, then finding the final velocity and using this to find work and then force, but it doesn't work. I need some help.

 

[PhanthomJay]

Please show how you calculated initial and final energies so we can see where you may have gone wrong. You don't have to find the 'final' energy at the water surface (although it's OK to do so), but you can find the final energy at the rest point below the water surface, and save a step.

 

[dmatador]

sorry about the notation...

(m)(g)(h_f) + (.5)(m)(v_f)^2 = (m)(g)(h_i) + (.5)(m)(v_i)^2

I then eliminated the m's, the terms (m)(g)(h_f) and (.5)(m)(v_i)^2 because the final height is zero and the initial velocity is zero. I then just solved for v_f, the final velocity.

Then I used W = (m)(g)(h_f) + (.5)(m)(v_f)^2 - (m)(g)(h_i) - (.5)(m)(v_i)^2

This is because once the swimmer hits the water, there is a change in total energy. I used the final velocity, v_f, from the other equation as v_i in this one. This is because she hits the water with this speed. I then used 0 as initial height h_i to eliminate the term (m)(g)(h_i) and v_f = 0 to eliminate (.5)(m)(v_i)^2. I then solved for W and divided this by the distance 1.11 done by this work to get the force.

 

[PhanthomJay]

You seem to be on the right track, but you are not showing your calcs. You may have made a math error, or perhaps you slipped up on a minus sign when calculating the potential energy at the 'rest' position.

 

[rwisz]

The problem of conservative and non-conservative forces is a fundamental concept in physics that is crucial for understanding the behavior of objects in motion. In this specific scenario, the 65.1 kg person jumping off a 3.04 m-high tower and coming to rest 1.11 m under the surface of water raises the question of the magnitude of the average force exerted by the water on the diver.

Firstly, it is important to note that a force is considered conservative if the work done by the force on an object is independent of the path taken by the object. On the other hand, a non-conservative force is one in which the work done by the force depends on the path taken by the object.

In this case, the force exerted by the water on the diver is a non-conservative force. This is because the work done by the water on the diver will depend on the path taken by the diver through the water. For example, if the diver were to enter the water at a different angle or with a different velocity, the work done by the water would be different.

To determine the magnitude of the average force exerted by the water on the diver, we can use the concept of work and energy. As the diver jumps off the tower, they possess potential energy due to their position above the water. As they descend, this potential energy is converted into kinetic energy. When the diver enters the water, they come to rest, meaning that all of their kinetic energy has been dissipated. This means that the work done by the water on the diver is equal to the change in the diver's kinetic energy.

Using the equation for potential energy (PE = mgh) and kinetic energy (KE = 1/2mv^2), we can set up the following equation:

mgh = 1/2mv^2

Where m is the mass of the diver, g is the acceleration due to gravity, h is the height of the tower, and v is the final velocity of the diver just before entering the water.

Solving for v, we get v = sqrt(2gh).

Now, using the equation for work (W = Fd) and substituting in the values we know (W = mgh), we can solve for the force exerted by the water on the diver:

F = W/d = mgh/d = (65.1 kg)(9.8 m/s^2)(3.04 m)