# Circular motion: net work after one period

• nx01
In summary, a 40 kg child sitting 6.0 m from the center of a merry-go-round with a constant speed of 6.0 m/s will experience a net work of 0 J after making one complete circle on the merry-go-round due to the perpendicular nature of the centripetal force and displacement. This can also be shown through the use of equations such as the circumference formula and the relationship between acceleration, force, and mass.

## Homework Statement

"A 40 kg child sitting 6.0 m from the center of a merry-go-round has a constant speed of 6.0 m/s. The net work (in Joules) done on the child after making one complete circle on the merry-go-round is?"

a=V^2/r
F=ma
C=2pi*r

## The Attempt at a Solution

C ≈ 37.7 m
a = 6 m/s
F at a point = (40)(6) = 240 N
Net work ≈ (240)(37.7) ≈ 9048 J

My question is, is the net work actually 0 J after one full rotation on the merry-go-round, since force is a vector quantity, and the force in one-half of the circular motion negates the force in the other half for each point?

You are right and you are wrong... the work is indeed zero, but actually not only on a full rounf, every time... indeed the work is the scalar product of the force times the displacement vector... and in an uniform circular motion the acceleration (and hence the force) is the centripetal one only, and is perpendicular ALWAYS to the displacement, so that the scalar product is identically zero

Thank you :)

## 1. What is circular motion?

Circular motion is a type of motion in which an object moves along a circular path. This means that the object maintains a constant distance from a fixed point, known as the center of the circle, while continuously changing direction.

## 2. What is net work in circular motion?

Net work in circular motion is the total amount of work done on an object after one full rotation around the circle. It takes into account both the magnitude and direction of the forces acting on the object.

## 3. How is net work calculated in circular motion?

The formula for calculating net work in circular motion is: W = Frcosθ, where W is the net work, F is the force acting on the object, r is the radius of the circular path, and θ is the angle between the force and the displacement of the object.

## 4. What is the relationship between net work and kinetic energy in circular motion?

In circular motion, the net work done on an object is equal to the change in kinetic energy of the object. This means that if there is a net work on the object, there will be a change in its speed or direction of motion.

## 5. Can net work be negative in circular motion?

Yes, net work can be negative in circular motion. This occurs when the force and displacement are in opposite directions, resulting in a negative value for net work. This means that the object loses kinetic energy and its speed decreases.