# Newton's Second Law -- Accelerations in a pulley system

#### Jonathan Schierl

1. The problem statement, all variables and given/known data
A 20-kg block with a pulley attached slides along a frictionless ledge. It is connected by a massless string to a 5.0-kg block via the arrangement shown in Figure. (a) draw complete free body diagrams for the masses and Find (b) the acceleration of each block and (c) the tension in he connecting string.

2. Relevant equations
net force= ma
Fweight=ga
Fnormal=Fweight

3. The attempt at a solution
aTension=aTension
Fweight-Ftenison=5a
Ftension=20a
Fweight-20a=5a
ga=25a

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#### gneill

Mentor
Hi Jonathan, Welcome to Physics Forums.

The problem mentions a figure that is absent from your post. Without it it would be difficult to solve the problem or evaluate your solution efforts. Can you post the image? Did you have a particular question about the work you've shown?

#### Jonathan Schierl

1. The problem statement, all variables and given/known data
A 20-kg block with a pulley attached slides along a frictionless ledge. It is connected by a massless string to a 5.0-kg block via the arrangement shown in Figure. (a) draw complete free body diagrams for the masses and Find (b) the acceleration of each block and (c) the tension in he connecting string.

2. Relevant equations
net force= ma
Fweight=ga
Fnormal=Fweight

3. The attempt at a solution
aTension=aTension
Fweight-Ftenison=5a
Ftension=20a
Fweight-20a=5a
ga=25a

#### gneill

Mentor
How does the pulley arrangement affect the relative rates of motion of the two blocks (do they both experience the same acceleration)? How does the pulley arrangement affect the net force delivered through string tension to each block?

In other words, does mechanical advantage play a role in this problem? If so, does your current work reflect this?

#### Jonathan Schierl

They both experience the same acceleration. The tension pulling both blocks will be the same because the string is massless

#### Jonathan Schierl

I don't believe mechanical advantage would play a role in this problem.

#### gneill

Mentor
They both experience the same acceleration. The tension pulling both blocks will be the same because the string is massless
I don't believe mechanical advantage would play a role in this problem.
Better check again!

Make yourself a sketch of just the block on the horizontal surface's pulley and its string connections. Suppose the pulley moves distance x to the right. How far does the top string have to move to take up the slack created?

#### Jonathan Schierl

No it actually doesn't play a role in this problem. We havent learned that yet.

#### gneill

Mentor
No it actually doesn't play a role in this problem. We havent learned that yet.
Nevertheless, solving this problem requires that you take into account the relative motions of the two blocks and the sum of tension forces at each block. If the problem requires concepts that you haven't learned yet, you should speak to your instructor.

"Newton's Second Law -- Accelerations in a pulley system"

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