Question

A body of mass m is moving in a horizontal circle of radius r with constant speed v. The force on the body is mv^2/r and is directed towards centre.

Calculate the work done on the object when it moves through a distance which is:

1. 1/2 The circumference of the circle
2. 1/4 the circumference of the circle
3. 3/4 the circumference of the circle
4.complete circumference of the circle.

Answer 1

Answer on Question #39840, Physics, Other

Question:

A body of mass $m$ is moving in a horizontal circle of radius $r$ with constant speed $v$. The force on the body is $mv^2/r$ and is directed towards centre.

Calculate the work done on the object when it moves through a distance which is:

1. 1/2 The circumference of the circle

2. 1/4 the circumference of the circle

3. 3/4 the circumference of the circle

4. complete circumference of the circle.

Answer:

Mathematically, work can be expressed by the following equation:

$$W = \int \vec{F} \vec{d} l = \int \vec{F} \vec{v} dt$$

where $\vec{F}$ is the force, $\vec{d}l$ is the displacement, $\vec{v}$ is velocity.

But force and velocity are perpendicular, therefore $\vec{F}\vec{v} = Fv\cos 90{}^{\circ} = 0$. So, work equals 0 for all distances.

Answer: 1,2,3,4: 0