A 67.7 kg person jumps from rest off a 3.11 m-high tower straight down into the water. Neglect air resistance during the descent. She comes to rest 1.04 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.

Well, let's dive into this problem! The first thing we need to do is determine the work done by the water on the person. We can use the work-energy principle for that. Now, the work done by a nonconservative force (like the water) is equal to the change in mechanical energy.

We can begin by calculating the potential energy the person has just before hitting the water, using the formula mgh, where m is the mass (67.7 kg), g is the acceleration due to gravity (9.8 m/s²), and h is the height (3.11 m). The potential energy is calculated as follows:

Potential energy = mgh
= (67.7 kg)(9.8 m/s²)(3.11 m)

Now, let's determine the change in mechanical energy. Since the person comes to rest 1.04 m below the surface of the water, there is a decrease in potential energy. The change in mechanical energy is:

Change in mechanical energy = mgh1 - mgh2

Where h1 is the initial height and h2 is the final height. So the change in mechanical energy is:

Change in mechanical energy = (67.7 kg)(9.8 m/s²)(3.11 m) - (67.7 kg)(9.8 m/s²)(1.04 m)

Now that we have the change in mechanical energy, we can use the work-energy principle to find the work done by the water. According to the work-energy principle:

Work done by water = Change in mechanical energy

So, the magnitude of the average force that the water exerts on the diver is equal to the work done by the water divided by the distance the diver traveled.

To find the work done, we multiply the change in mechanical energy by -1 (since the work done by the water is negative, as it opposes motion), and then divide by the distance traveled.

Average force = -Change in mechanical energy / distance traveled

Now that we have all the necessary information, we can go ahead and calculate the magnitude of the average force. But before we do that, let me throw in a little joke for you:

Why don't scientists trust atoms?

Because they make up everything!

Now back to business! Let's calculate the magnitude of the average force:

Average force = -Change in mechanical energy / distance traveled
= -[(67.7 kg)(9.8 m/s²)(3.11 m) - (67.7 kg)(9.8 m/s²)(1.04 m)] / 1.04 m

Simplifying this expression will give us the magnitude of the average force.

Remember, this is just a mathematical calculation, so don't dive too deep into it!

To determine the magnitude of the average force that the water exerts on the diver, we can use the principle of conservation of energy.

When the person jumps off the tower, they convert their potential energy into kinetic energy as they fall towards the water. This energy is then transferred to the water, causing the person to come to rest.

First, let's calculate the potential energy of the person at the top of the tower using the formula:

Potential Energy = mass * gravity * height

where mass = 67.7 kg, gravity = 9.8 m/s^2, and height = 3.11 m.

Potential Energy = 67.7 kg * 9.8 m/s^2 * 3.11 m
= 2021.7 Joules

Next, let's calculate the potential energy of the person at the point where they come to rest under the water's surface. Since the person is at rest, their kinetic energy is zero, and all their initial potential energy is converted into potential energy related to their depth in the water:

Potential Energy = mass * gravity * depth

where depth = 1.04 m.

Potential Energy = 67.7 kg * 9.8 m/s^2 * 1.04 m
= 695.6216 Joules

The work done by the water to bring the person to rest is equal to the difference in potential energy:

Work done by water = Initial Potential Energy - Final Potential Energy
= 2021.7 Joules - 695.6216 Joules
= 1326.0784 Joules

The average force exerted by the water can be determined by dividing the work done by the distance traveled:

Average Force = Work done by water / distance
= 1326.0784 Joules / 3.11 m
= 426.021 N

Therefore, the magnitude of the average force that the water exerts on the diver is approximately 426.021 Newtons.

2753.3 J

Lost potential energy

= M*g*(3.11 + 1.04)= M*g*(4.15 m)
= work done against friction
= Fav*(1.04 m)

(There is zero kinetic energy at the beginning of the dive and the greatest underwater depth)

Fav = (4.15/1.04)*M*g
= 734 N