# Two Blocks and a Pulley Friction Problem

• joemost12
In summary, the conversation involves solving for the acceleration of a 5.0 kg block on a smooth horizontal table with a 12 kg block on top, given a diagram and relevant equations. The solution involves calculating the forces on each block and setting up a system of equations to solve for the acceleration. The final answer is 1.82 m/s^2.
joemost12

## Homework Statement

System comprised blocks, a light frictionless pulley and connecting ropes (see diagram). The 9.0kg block is on a perfectly smooth horizontal table. The surfaces of the 12kg block are rough, with μk = .2 between the two blocks. If the 5.0 kg block accelerates downward when it is released, find its acceleration

Fairly certain my solution is correct, just would love a second opinion!

Diagram:

http://i.imgur.com/6k5Im7W.png

## The Attempt at a Solution

So for the 12kg Block my reasoining for its forces was:
Fnet = Ffriction - T1 = Ma = 0
Fnormal = (12kg)(9.8 m/s^2 _ = 117.6
ForceFriction = (.2)(11.6) = 23.52 N

Then for the 9 KG block:
Fnet = T2 - ForceFriction
T2 - 23.52N = Ma
T2 - 23.52N = (9kg)a
23.52-T2 = (9 kg) a

Then finally for the hanging 5.0 KG block:
T2 - Fg = ma
T2 - (5)(9.8) = (5)a
T2 - 49N = 5(a)

Then I simply solved the system of equations to find the value of A

Set two equations for the 9kg and the 5kg block in terms of a

(T2 - 49N)/5 kg = (23.52N - T2)/9kg
Solving to find that T2 = 39.9
Then simply plug that value back into T2 - 49N = 5a

a = 1.82 m/s^2

Looks good.

gneill said:
Looks good.
Great. Thanks

## 1. What is a pulley and how does it work in this problem?

A pulley is a simple machine that consists of a wheel with a groove around its circumference and an axle. In the context of a Two Blocks and a Pulley Friction Problem, a pulley is used to change the direction of a force and to distribute the force evenly across the two blocks.

## 2. What is friction and why is it important in this problem?

Friction is the resistance force that occurs when two surfaces come in contact with each other. It is important in this problem because it affects the motion and stability of the blocks on the pulley. Without friction, the blocks would slide and fall off the pulley due to the force of gravity.

## 3. How do you calculate the friction force in this problem?

The friction force can be calculated using the formula F = μN, where F is the friction force, μ is the coefficient of friction, and N is the normal force. In this problem, the normal force is equal to the weight of the block, and the coefficient of friction can be determined based on the materials of the surfaces in contact.

## 4. Can the mass of the blocks affect the friction force in this problem?

Yes, the mass of the blocks can affect the friction force. The friction force is directly proportional to the normal force, which is equal to the weight of the block. Therefore, a heavier block will have a greater friction force compared to a lighter block.

## 5. How does the angle of the pulley affect the friction force in this problem?

The angle of the pulley does not directly affect the friction force. However, it can affect the normal force and the tension in the rope, which can indirectly affect the friction force. As the angle of the pulley increases, the normal force and the tension in the rope also increase, resulting in a greater friction force.

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