# Friction of Two Blocks and Rope Problem

• FairyChatMan
In summary, the problem involves two blocks (A and B) with weights of 80 lb and 120 lb respectively, positioned on an inclined plane. Block A is attached to a rope and does not slide or fall from block B. The task is to calculate the smallest force that needs to be applied on block B for it to not move parallel to the inclined plane. The equation used is F = fN, where N = Wcos\theta, and various frictional forces are calculated for different parts of the system. However, the problem may not be stated and illustrated correctly, as the angle between the rope and wall is not given and it does not seem possible for block B to move as shown in the setup.

## Homework Statement

Two blocks are positioned according to the figure. Block A (80 lb) is attached to a rope as such that it doesn't slide or fall from block B (120lb). Compute the smallest value of Force to be applied on Block B for it to not move parallel to the inclined plane.

## Homework Equations

F = fN
N = Wcos$$\theta$$

## The Attempt at a Solution

Here's how I did, I assumed that Block B is sliding downwards parallel to the inclined plane.

Then I compute the Frictional force between block A and B, so

W = 80 lb
N = 80cos20
Friction forceA&B = 0.2(80cos20) direction is upwards parallel to inclined plane, because it will resist the downward sliding motion of Block B.

Then compute for Friction force between Block B and plane, so

W = 80 +120 (is this correct?)
N = 200cos20
Friction forceB&plane = 0.2(200cos20) direction same with previous Ff.

Then I compute for the sliding magnitude of Block B, assuming it will slide because of none external force acting on it other than friction

F = 120sin20 (force not applying frictions)
F2 = 120sin20 - (0.2(80cos20) + 0.2(200cos20)) = Answer

I equate F2 as my answer because that's the only force left in the system needed to be countered... so my force needs to be acting upward...

When I substituted all values... it gives me a negative answer force... so does that mean... I'm wrong?

First off, the angle between the rope and wall is not given. If as shown, it increases the normal forces you calculated, and you would need to know that angle. But secondly, it doesn't appear that the lower block can move as shown in the setup, even if the rope was parallel to the incline. Is this problem stated and illustrated correctly?

## 1. What is friction and how does it affect the movement of two blocks connected by a rope?

Friction is a force that resists the relative motion between two surfaces in contact. In the case of two blocks connected by a rope, friction can prevent the blocks from sliding against each other or against the surface they are resting on.

## 2. How does the coefficient of friction impact the movement of the blocks?

The coefficient of friction is a measure of the roughness or smoothness of the surfaces in contact. A higher coefficient of friction means there is more resistance to motion, while a lower coefficient of friction means there is less resistance. In the case of the two blocks and rope problem, a higher coefficient of friction between the blocks or between the blocks and the surface will result in more friction and slower movement.

## 3. Can the tension in the rope affect the friction between the blocks?

Yes, the tension in the rope can affect the friction between the blocks. When the tension is high, the blocks are pressed together more tightly, increasing the friction between them. This can also increase the friction between the blocks and the surface they are resting on.

## 4. How does the mass of the blocks impact the friction between them?

The mass of the blocks does not directly impact the friction between them. However, a heavier block may have a greater normal force (force perpendicular to the surface) which can increase the friction between the block and the surface it is resting on.

## 5. What other factors besides friction can affect the movement of the blocks?

Other factors that can affect the movement of the blocks include the angle of the rope, the surface the blocks are resting on, and the shape and weight distribution of the blocks. These factors can impact the tension in the rope and the normal force between the blocks and the surface, which in turn can affect the friction and overall movement of the blocks.