# Is the Frictional Force on a Sloped Block Greater Than Its Weight?

• 1Deag4Days
In summary, the conversation discusses the frictional force acting on a block at rest on a rough incline. The options for the magnitude of the frictional force are given as greater than, equal to, or less than the weight of the block. The correct equation for the frictional force is MG/sin(theta), which is equal to the weight along the slope. It is determined that the frictional force should be equal to the weight of the block, and there was an error in decomposing the gravitational force vector.
1Deag4Days

## Homework Statement

A block is at rest on a rough incline .
The frictional force acting on the block, along the incline, is
A) greater than the weight of the block.
B) equal to the weight of the block.
C) zero.
D) less than the weight of the block.

## The Attempt at a Solution

The frictional force should be equal to the Weight along the slope so MG/sin(theta) so shouldn't the frictional force be greater than the weight of the block?

The weight along the slope is greater than the total weight?

How do you get MG/sin(theta)? That would imply, as the angle theta goes to zero, the weight along the slope goes to infinity. Is that reasonable?

I know I'm doing something wrong but i don't know what

#### Attachments

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Nvm I got it I was decomposing my gravitational force vector incorrectly

Your reasoning is correct. The correct answer would be option A) greater than the weight of the block. The frictional force acts in the opposite direction of the block's motion, and in order for the block to be at rest on the slope, the frictional force must be greater than the component of the weight of the block acting along the slope. This ensures that the block does not slide down the slope.

## 1. What causes a block to remain at rest on a slope?

The block remains at rest on a slope due to the balance of forces acting on it. The downward force of gravity is counteracted by the normal force from the surface of the slope, as well as the frictional force between the block and the slope.

## 2. How does the slope angle affect the block at rest?

The steeper the slope angle, the greater the force of gravity pulling the block downwards. This increases the normal force required to balance it, making it more difficult for the block to remain at rest.

## 3. Can a block remain at rest on a frictionless slope?

No, a block cannot remain at rest on a frictionless slope. Without friction, there is no opposing force to balance the downward force of gravity, causing the block to slide down the slope.

## 4. What is the role of surface roughness in keeping a block at rest on a slope?

Surface roughness plays a crucial role in keeping a block at rest on a slope. A rough surface provides more friction, which helps to increase the normal force and prevent the block from sliding down the slope.

## 5. How does the mass of the block affect its stability on a slope?

The mass of the block does not directly affect its stability on a slope. However, a more massive block will have a greater downward force of gravity, requiring a larger normal force and more friction to keep it at rest on the slope.

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