What is the Relationship Between Velocity, Radius, and Force in a Pulley System?

[AN630078]

Homework Statement

Hello, I have been practising some of the past Oxford PAT papers and have come across a question with the mark scheme which I do not understand. I have attached a photograph of it.
Why does the velocity equal 3*initial velocity for part b? Why is the velocity not 0.5ms^-1?

Relevant Equations

W=v/r

B)
W=v/r
v=?
r=diameter/2=0.025m

 

[Halc]

Why does the velocity equal 3*initial velocity for part b?

That's just the way the pulleys are strung. For every 3 units of motion of the string being wound by the motor, the lifted mass rises 1 unit.
The problem seems to concern a steady rate of pull, without initial acceleration or any kind of 'initial state' defined.

Why is the velocity not 0.5ms^-1?

That's the velocity of the mass m, not the rate at which the reel is winding the string.

 

[AN630078]

That's just the way the pulleys are strung. For every 3 units of motion of the string being wound by the motor, the lifted mass rises 1 unit.
The problem seems to concern a steady rate of pull, without initial acceleration or any kind of 'initial state' defined.

That's the velocity of the mass m, not the rate at which the reel is winding the string.

Oh ok thank you very much for your reply. I did not know that, so is it because there are three pulleys in this system to lift the mass by 1 unit. But for example if there were only two pulleys for the string to be wound around would the velocity be found by v=2u?
Right ok, I see that it is the velocity of the mass not the velocity of the winding.

 

[Halc]

Oh ok thank you very much for your reply. I did not know that, so is it because there are three pulleys in this system to lift the mass by 1 unit. But for example if there were only two pulleys for the string to be wound around would the velocity be found by v=2u?

It is not so much the number of pulleys but the number of strings between the pulleys. There are 3 strings pulling up on m, and the force needs to balance. So there is 980 N pulling down, so each string must be pulling up at 327N. The 333 answer seems to assume a round 10 m/sec gravitational acceleration.

 

[AN630078]

It is not so much the number of pulleys but the number of strings. There are 3 strings pulling up on m, and the force needs to balance. So there is 980 N pulling down, so each string must be pulling up at 327N. The 333 answer seems to assume a round 10 m/sec gravitational acceleration.

Oh ok I think I understand it far better now Thank you for your help