Work Circular Motion Homework: Calculate Total Work Done on Ball

[Heat]

Homework Statement

A ball of mass 0.765 kg is tied to the end of a string of length 1.59 m and swung in a vertical circle.

a)During one complete circle, starting anywhere, calculate the total work done on the ball by the tension in the string.

b)During one complete circle, starting anywhere, calculate the total work done on the ball by gravity.

c)Repeat part (a) for motion along the semicircle from the lowest to the highest point on the path.

d)Repeat part (b) for motion along the semicircle from the lowest to the highest point on the path.

The Attempt at a Solution

I know that for part a and b it will be 0, because the displacement is 0, according to W = F * s

However, I don't understand part c.

the displacement is 4.995.

 

[stunner5000pt]

what is happening to the rock?? What is occurring to its height??

What kind of energy is being imparted to the stone as a result of this height change?

What is the height change?

 

[Heat]

what is happening to the rock?? it's moving up
What is occurring to its height?? increasing upwards

What kind of energy is being imparted to the stone as a result of this height change? gravity is pulling down, and tension is pulling it toward the center I believe

What is the height change? 4.995

 

[stunner5000pt]

what is happening to the rock?? it's moving up
What is occurring to its height?? increasing upwards

What kind of energy is being imparted to the stone as a result of this height change? gravity is pulling down, and tension is pulling it toward the center I believe

What is the height change? 4.995

For part c then
what is the angle between the displacement of the rock and the force of tension?? Consider very small displacements

 

[Heat]

the angle theta is 3.141509434

 

[stunner5000pt]

the angle theta is 3.141509434

why is that?

 

[Heat]

displacement is 4.995 right? (unless this is incorrect).

length of string is 1.59m

4.995m = 1.59(theta)

 

[stunner5000pt]

displacement is 4.995 right? (unless this is incorrect).

length of string is 1.59m

4.995m = 1.59(theta)

we'll talk about how you got the4.995 later.
How do you figure theta from there??

Think about it... the tension is pulling the rock inward. The rock is moving in a circle. If something is moving in a circle what is its instantaneous displacement?? Along what direction is the instantaneous displacement?? What is the angle between this instantaneous displacement and the force of tension??

 

[Heat]

if something is moving in a circle, then the displacement would be in radians. instantaneous displacement

the direction of the instantaneous displacement is upwards.

The angle is pi/2 or 90 degrees.

 

[stunner5000pt]

if something is moving in a circle, then the displacement would be in radians. instantaneous displacement

the direction of the instantaneous displacement is upwards.

The angle is pi/2 or 90 degrees.

Good. SO the angle between the force of tension and the displacement is zero. Hence what is the work done by the tension?

$$W = F d \cos \theta = F d \cos \frac{\pi}{2} = ?$$

 

[Heat]

0.

that would be part c.

now would part d be similar.