relationship between coefficient of friction and angle of surface to horizontal on which body is being pushed upwards

The coefficient of friction (usually denoted as μ) is a measure of the frictional resistance between two surfaces in contact. When a body is being pushed or pulled on an inclined surface, the angle of the surface to the horizontal (θ) plays a significant role in determining the frictional force.

The relationship between the coefficient of friction (μ), the angle of the surface to the horizontal (θ), and the normal force (N) can be described using the following equation:

Firctional Force = μ * N

The normal force (N) is affected by the angle of the surface. When an object is on an inclined plane, the normal force is less than the weight of the object (mg), and it can be calculated as:

N = mg * cos(θ)

So, the frictional force on an inclined surface can be expressed as:

Firctional Force = μ * mg * cos(θ)

From this equation, you can see that as the angle of the surface to the horizontal (θ) increases, the cosine of θ decreases. Therefore, the normal force (N) decreases, which, in turn, affects the frictional force (F_friction). As a result:

• When θ is 0 (horizontal surface), the normal force is equal to the weight of the object, and the frictional force is at its maximum = μ * mg
• As θ increases (surface becomes inclined), the normal force decreases, leading to a decrease in the maximum possible frictional force.

In summary, the angle of the surface to the horizontal affects the normal force, which, in turn, affects the frictional force between the object and the surface. As the angle increases, the available frictional force decreases, and this can impact the motion or stability of the object on the inclined surface.