# Frictionless Equilibrium of Block and Wedge System

• Guppy
In summary, the conversation is about a block resting on a rough wedge on a rough horizontal floor, and the frictional force exerted by the floor on the wedge when the whole system is at rest. The system is in equilibrium with only gravity and the normal force acting on it. If the floor is smooth, the block will still stay the same way as on a rough floor since no frictional force is needed.
Guppy
Hello, I am new member here.
I would like to know how should I handle this question:

A block of mass 2.5kg rests on the rough surface of a wedge, which in turn rests on a rough horizontal floor. What is the frictional force exerted by the floor on the wedge if the whole system is at rest?

The height of the wedge is 30cm and the length is 40cm (Side view)

Consider that the system of "block + wedge" is in equilibrium: the net force on it must be zero. Besides the force that the floor exerts, what forces act on that system? And what frictional force must the floor exert to couteract those forces?

The system of Block & Wedge is in equilibrium, so the whole system is balanced, and the only force acting on the floor is the Mg of the whole block & wedge system, therefore no frictional force is exerted by the floor on the wedge as there is no frictional force exerted by the wedge on the floor, isn't it?

By the way, if it's a smooth floor, the block will also stay the same way as the above case?

Guppy said:
The system of Block & Wedge is in equilibrium, so the whole system is balanced, and the only force acting on the floor is the Mg of the whole block & wedge system, therefore no frictional force is exerted by the floor on the wedge as there is no frictional force exerted by the wedge on the floor, isn't it?
This is true. Here's how I would word it. Other than the floor (which merely exerts a passive force), the only force on the system (block + wedge) is gravity. Since the weight of the system acts straight down, the only force that the floor applies to counter it is the normal force--no frictional force is needed.

By the way, if it's a smooth floor, the block will also stay the same way as the above case?
Yes. Since no frictional force is needed, it doesn't matter if the floor is smooth or not. (Things would change if the mass were able to slide down the wedge.)

gracy

## 1. What is a block inclined on a wedge?

A block inclined on a wedge refers to a system where a block is resting on a sloped surface known as a wedge. This creates an inclined plane and allows for the block to be moved up or down the wedge.

## 2. What is the purpose of studying block inclined on a wedge?

Studying block inclined on a wedge helps us understand the principles of mechanics, such as forces, motion, and energy. It also has real-world applications, such as in construction and engineering.

## 3. How does the angle of inclination affect the block on a wedge?

The angle of inclination determines the amount of force required to move the block up or down the wedge. The steeper the angle, the greater the force needed to overcome gravity and friction.

## 4. What are the forces acting on a block inclined on a wedge?

The forces acting on a block inclined on a wedge include the weight of the block, the normal force from the wedge, and the force of friction. Other external forces, such as a pushing or pulling force, may also be present.

## 5. How can we calculate the work done on a block inclined on a wedge?

The work done on a block inclined on a wedge can be calculated by multiplying the force applied to move the block by the distance it moves in the direction of the force. This is represented by the equation W = Fd, where W is work, F is force, and d is distance.

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