Block, Cart, and Pulley Question

In summary: When you combine the two masses to find the acceleration using F=ma because acceleration is uniform through the system.
  • #1
r34racer01
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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

 
Last edited:
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  • #2
Welcome to PF!

r34racer01 said:
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! :smile:

Hint: work done by gravity = change in PE …

so how much mass is having its PE changed? :wink:
 
  • #3


tiny-tim said:
Hi r34racer01! Welcome to PF! :smile:

Hint: work done by gravity = change in PE …

so how much mass is having its PE changed? :wink:

Is it m2 or both masses?
 
  • #4
r34racer01 said:
Is it m2 or both masses?

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

So how much mass is changing height? :wink:
 
  • #5
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?
 
  • #6
r34racer01 said:
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! :biggrin:
 
  • #7
Ok so I got Wg =20.601, But now I'm a little confused with finding the change in KE.
 
  • #8
r34racer01 said:
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 :smile:
 
  • #9
tiny-tim said:
work done by gravity = change in PE = change in KE :smile:

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?
 
  • #10
r34racer01 said:
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! :smile:

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? :wink:

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! :biggrin:
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 :wink:

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. :smile:
 
  • #11
tiny-tim said:
HI r34racer01! :smile:

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? :wink:

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! :biggrin:


i] it's 8.24, not 8.32 :wink:

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. :smile:

Wow thx, but how is 8.24 and not 8.32?
 
  • #12
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
 
  • #13
r34racer01 said:
Wow thx, but how is 8.24 and not 8.32?

2.872 = 8.24 :wink:

how did you get 8.32?
 

Related to Block, Cart, and Pulley Question

1. What is a block, cart, and pulley question?

A block, cart, and pulley question is a physics problem that involves a block resting on a frictionless surface, connected to a cart by a rope or cable that passes over a pulley. This setup allows for the application of the principles of mechanics, such as Newton's laws of motion, to determine the motion and forces acting on the block and cart system.

2. How do you solve a block, cart, and pulley question?

To solve a block, cart, and pulley question, you must first draw a free-body diagram to identify all the forces acting on the system. Then, use Newton's second law (F=ma) and the equations of motion to analyze the forces and determine the acceleration and motion of the system. Finally, check your solution to make sure it satisfies all the given conditions of the problem.

3. What are the common assumptions made in a block, cart, and pulley question?

Some common assumptions made in a block, cart, and pulley question include the block and cart having negligible mass, the surface being frictionless, and the pulley being massless and frictionless. These assumptions simplify the problem and allow for easier analysis using the principles of mechanics.

4. How does the number of pulleys affect the block, cart, and pulley question?

The number of pulleys in a block, cart, and pulley question affects the mechanical advantage of the system. With more pulleys, the force required to move the system decreases, but the distance the rope or cable must be pulled increases. This relationship is described by the equation Fout = Fin/n, where Fout is the output force, Fin is the input force, and n is the number of pulleys.

5. What real-life applications use the principles of a block, cart, and pulley system?

Block, cart, and pulley systems are commonly used in engineering and everyday life. Examples include elevators and cranes, where the pulleys allow for heavy objects to be lifted with less force, and exercise equipment, such as weight machines, which use pulleys to provide resistance. They are also used in various industrial and manufacturing processes, such as conveyor belts and assembly line systems.

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