A person is riding on a Ferris wheel of radius R. He starts at the lowest point of the wheel. When the wheel makes one complete revolution, is the net work done by the gravitational force positive, zero, or negative?
Do you need to know how the speed of the person changed before you can answer the question?
Suppose he started at the highest point of the wheel. What is the net work done by the gravitational force when he reaches the lowest point?
zero. potential energy in gravity is m g h
If you come back to the same h, no net work was done.
(you had to put work in going up, you took it out coming down.)
In the second part it is m g htop -mghbottom
= m g (2R)
Well, well, well, let's take a spin on this question! When the person starts at the lowest point of the Ferris wheel and completes one revolution, the net work done by the gravitational force is indeed... drumroll please... zero! Why, you ask? Well, gravity's pulling straight down, and the person ends up back where they started. It's like being stuck in a loop of getting nowhere! No net change in position means no net work done!
As for the second part, if the person starts at the highest point and lands on the lowest point, things get interesting. Gravity is doing its job, pulling the person down while they move in the same direction. This time, gravity does positive net work! It's like giving a gentle push to help them along on their thrilling ride. So, in this case, the net work done by the gravitational force is positive. Gravity's getting in on the fun, and who doesn't love some positive energy?
To determine if the net work done by the gravitational force is positive, zero, or negative when a person completes one revolution on a Ferris wheel, we need to consider the change in height and the direction of the gravitational force.
When the person starts at the lowest point of the wheel, the net work done by the gravitational force can be determined by the formula:
Net work = force x displacement x cos(theta)
In this case, the force and displacement are in the same direction, as gravity pulls downwards and the person moves downwards. The angle (theta) between the force and the displacement is 0 degrees, as they are parallel.
Since cos(0) = 1, the net work done by the gravitational force is positive:
Net work = force x displacement x cos(theta) = force x displacement x cos(0) = force x displacement x 1 = force x displacement
Therefore, when the person starts at the lowest point, the net work done by the gravitational force is positive.
Now, let's consider the scenario where the person starts at the highest point of the wheel and reaches the lowest point. In this case, the change in height is R (the radius of the Ferris wheel), as the person moves from the highest point to the lowest point. The force and displacement are in the opposite direction, as gravity pulls downwards while the person moves upwards. The angle (theta) between the force and the displacement is 180 degrees, as they are opposite and parallel.
Since cos(180) = -1, the net work done by the gravitational force is negative:
Net work = force x displacement x cos(theta) = force x displacement x cos(180) = force x displacement x -1 = -force x displacement
Therefore, when the person starts at the highest point and reaches the lowest point, the net work done by the gravitational force is negative.
To determine the net work done by the gravitational force on the person riding the Ferris wheel, we need to consider the change in potential energy of the person.
1. When the person starts at the lowest point of the Ferris wheel and makes one complete revolution, the net work done by the gravitational force is zero. This is because the gravitational force is perpendicular to the direction of motion at all points in the circular path. As a result, the gravitational force does not do any work on the person. The change in potential energy of the person is also zero since the height at the starting and ending points is the same.
2. If the person starts at the highest point of the Ferris wheel and reaches the lowest point, the net work done by the gravitational force is negative. This is because at the highest point, the person has maximum potential energy. As the person descends to the lowest point, the potential energy decreases. Since work is defined as the change in energy, the gravitational force does negative work on the person, resulting in a decrease in potential energy.