Block, Cart, and Pulley Question

[r34racer01]

A cart of mass M1 = 2 kg is attached to a block of mass M2 = 3 kg by a string that passes over a frictionless pulley. The system is initially at rest and the table is frictionless. After the block has fallen a distance h = 0.7 m

a) What is the work Wg done by gravity on the system?

b) What is the increase in kinetic energy DK of the cart-plus-block system?

c) What is the speed |v| of the cart-plus-weight system?

d) What is the work Ws done on the cart (not the block!) by the string?

e) What is the tension T in the string?

I'm really Lost. I can't even figure out what I did wrong when solving for Wg. I did
Wg = mgh = (5kg)(9.81)(0.7) = 34.335 and that wasn't right.

Homework Statement

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

Welcome to PF!

A cart of mass M1 = 2 kg is attached to a block of mass M2 = 3 kg by a string that passes over a frictionless pulley. The system is initially at rest and the table is frictionless. After the block has fallen a distance h = 0.7 m
…
I'm really Lost. I can't even figure out what I did wrong when solving for Wg. I did
Wg = mgh = (5kg)(9.81)(0.7) = 34.335 and that wasn't right.

Hi r34racer01! Welcome to PF!

Hint: work done by gravity = change in PE …

so how much mass is having its PE changed?

 

[r34racer01]

Hi r34racer01! Welcome to PF!

Hint: work done by gravity = change in PE …

so how much mass is having its PE changed?

Is it m2 or both masses?

 

[tiny-tim]

Is it m2 or both masses?

Gravitational PE (potential energy) is caused by change in height.

So how much mass is changing height?

 

[r34racer01]

Oh so it is m2, I forgot also that forces perpendicular to the object perform 0 work, so gravity does no work on m1 right?

 

[tiny-tim]

Oh so it is m₂, I forgot also that forces perpendicular to the object perform 0 work, so gravity does no work on m₁ right?

Bingo!

 

[r34racer01]

Ok so I got Wg =20.601, But now I'm a little confused with finding the change in KE.

 

[tiny-tim]

Ok so I got Wg =20.601, But now I'm a little confused with finding the change in KE.

work done by gravity = change in PE = change in KE

 

[r34racer01]

work done by gravity = change in PE = change in KE

Wow I didn't even realize that. So Wg = 20.601. And with that I was able to figure out that |v|=2.87.

So now I'm trying to figure out the work done by the string. We know that the speed is 2.87, so the KE of the cart is 8.32J. I thought I could do 20.601-8.32 to get Ws, but apparently that's wrong. So what should I be doing?

 

[tiny-tim]

Wow I didn't even realize that. So Wg = 20.601. And with that I was able to figure out that |v|=2.87.

HI r34racer01!

You didn't realize that? But it's so important …

work and energy are the same ("work-energy theorem") …

KE and PE are the same ("conservation of energy") …

see how neatly it all fits together?

It means that if you want to calculate the KE, say, it's sometimes easier to calculate either the PE or the work done, and use that instead!

So now I'm trying to figure out the work done by the string. We know that the speed is 2.87, so the KE of the cart is 8.32J. I thought I could do 20.601-8.32 to get Ws, but apparently that's wrong. So what should I be doing?

i] it's 8.24, not 8.32

ii] why do you want the work done … the question doesn't ask for it?

but it's equal to the KE anyway, which you now have.

Then you can find the tension by "reverse-engineering" from the work done.

 

[r34racer01]

HI r34racer01!

You didn't realize that? But it's so important …

work and energy are the same ("work-energy theorem") …

KE and PE are the same ("conservation of energy") …

see how neatly it all fits together?

It means that if you want to calculate the KE, say, it's sometimes easier to calculate either the PE or the work done, and use that instead!


i] it's 8.24, not 8.32

ii] why do you want the work done … the question doesn't ask for it?

but it's equal to the KE anyway, which you now have.

Then you can find the tension by "reverse-engineering" from the work done.

Wow thx, but how is 8.24 and not 8.32?

 

[aimslin22]

part e.

combine the two masses to find the acceleration using F=ma because acceleration is uniform through the system.

Then use one of the masses and F=ma to determine tension.

This equation would be set up like this:

Winner force - loser force = ma

 

[tiny-tim]

Wow thx, but how is 8.24 and not 8.32?

2.87² = 8.24

how did you get 8.32?