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Calculating the acceleration and kinetic energy of a bucket in a pulley system

  • Thread starter mmoadi
  • Start date
157
0
1. The problem statement, all variables and given/known data

A well pulley is constructed from wooden cylinder with a mass of 5 kg and a radius of 10 cm and a light handle. The bucket filled with water is hanging on the rope coiled to the cylinder has a mass of 7 kg.
- With how much acceleration does the bucket move if the handle breaks; the pulley is spinning with no friction?
- How much is the kinetic energy of the bucket after it falls for 1 m?

2. Relevant equations

F=ma
KE= mv²/2
PE= mgh

3. The attempt at a solution

First part: With how much acceleration does the bucket move if the handle breaks; the pulley is spinning with no friction?

m(1)= 5 kg, m(2)= 7 kg, g= 10 m/s²

(m(1) + m(2))*a= m(2)g
a= m(2)g / (m(1) + m(2)
a= 5.8 m/s²

ARE MY CALCULATIONS CORRECT?

Second part: How much is the kinetic energy of the bucket after it falls for 1 m?

KE= PE
mv²/2= mgh
v= sqrt(2gh)
v= 4.47 m/s

KE= mv²/2= 69.9 J

Are my calculations correct?

Thank you helping!
 

rl.bhat

Homework Helper
4,433
5
The equation for acceleration is wrong. Check it.
 
157
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Do I have to take into the consideration inertia and the torque of the pulley (I know the radius and the mass of the pulley) and develop it from there?:confused:

What about the second part? Is it correct?

Thank you for helping!
 
Last edited:
There is torque acting on the cylinder because of the tension in the rope.
 
157
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Please, can you give a hint how to apply the torque into the calculations? I'm really confused!?

I tried it like this:

For the bucket:
m(1)a= m(1)g - T

For the pulley:
Iα= Tr

I= 1/2m(2)r² and α= a/r

1/2m(2)r²*a/r = Tr → 1/2m(2)r= T

For the system:
1/2m(2)a + m(1)a = m(1)g -T + T
a= m(1)g / (m(1) + 1/2m(2))
a= 7 m/s²

I really need help with solving this problem. Thank you for helping!
 
Yes.

Now for the second part you just replace g with your new a.
 
157
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:biggrin: Thank you very much!:biggrin:

So the correct answer is: 49 J
 

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