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What is the work done on the ball by the tension in the string? (Physics)

A ball of mass m is attached to a string of length r and is swing in a horizontal circle with constant angular velocity ω. What is the work done on the ball by the tension in the string?

A: 2 πmr2ω2
B: πmr2ω2
C: 2 L mrω2
D: Zero

Please explain
Original post by Aalishan
A ball of mass m is attached to a string of length r and is swing in a horizontal circle with constant angular velocity ω. What is the work done on the ball by the tension in the string?

A: 2 πmr2ω2
B: πmr2ω2
C: 2 L mrω2
D: Zero

Please explain

It is A as work done is force x distance. The distance travelled is the circumference of one circle = 2(pi)r. Tension must = mw2r so

work done = 2(pi)r x mw2r = 2(pi)mw2r2
Reply 2
Avatar for oxe
oxe
6
I thought it was zero :s since no work done in the direction of the force since the ball is moving perpendicular to the force (ie no distance travelled in the direction of the force) but im not sure

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Reply 3
Avatar for Aalishan
Aalishan
OP
2
Original post by PhysicsProf
It is A as work done is force x distance. The distance travelled is the circumference of one circle = 2(pi)r. Tension must = mw2r so

work done = 2(pi)r x mw2r = 2(pi)mw2r2


You wrote tension must be mw2r
How is it?
Original post by Aalishan
You wrote tension must be mw2r
How is it?


The tension is providing the centripetal force required to turn the ball in a circle of radius r. So the tension must equal mv²/r or mw²r depending on what you are given in the question. In this case you have been given w so use F=mw²r.

So work done= Fxd where distance in this case is 2(pi)r. as T is providing the centripetal force T=mw²r so
work done=mw²r x 2(pi)r
work done= 2(pi)mw²r²
Reply 5
Avatar for Aalishan
Aalishan
OP
2
Thank you Sir!
Original post by Aalishan
A ball of mass m is attached to a string of length r and is swing in a horizontal circle with constant angular velocity ω. What is the work done on the ball by the tension in the string?

A: 2 πmr2ω2
B: πmr2ω2
C: 2 L mrω2
D: Zero

Please explain


The work done is 0 J.

You can understand this in at least two ways:

1) The tension and the velocity of the ball are always at right angles, so there is no component of tension in the direction of the velocity i.e. there is no component of tension in the direction of the displacement of the ball over an infinitesimal time period. Hence the infinitesimal work done over this period is:

dW=Fds=0ds=0dW =F ds = 0 ds = 0 J

But this is true at all times, so the tension can do no work over a non-infinitesimal time period.

2) Suppose on the contrary that the tension does work on the ball. Over a complete circuit, the energy of the ball would increase. Since the ball is travelling in a horizontal circuit, its GPE is constant. Hence, its KE must increase over a complete circuit, and hence its velocity and therefore angular velocity must increase. But this contradicts the statement that it moves with constant angular velocity, so the tension must do no work on the ball.

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