How Is Frictional Force Doing Work on a Sliding Block?

[c4iscool]

Homework Statement

A 1.6-kg block slides down a plane (inclined at 25° with the horizontal) at a constant speed of 2.0 m/s. At what rate is the frictional force doing work on the block?

Homework Equations

The Attempt at a Solution

I think that you have to find the potential energy, kinetic energy, 1/2mv^2 , and the force acting on the block, f =m* g. then subtracting the potential from the kinetic and force and this should give me the frictional force acting on the block, right?

 

[rock.freak667]

well you have no information to find the potential energy, so you'll need to consider forces.

If it moves at a constant speed of 2.0 m/s what does this imply about the resultant force on it? (Newton's First law can aid you here)

When you know this, just consider all the forces parallel to the plane.

 

[Moetasim]

Your approach is on the right track. To find the rate at which the frictional force is doing work on the block, you can use the equation W = Fd, where W is work, F is force, and d is distance. In this case, the distance is the length of the inclined plane, which can be found using trigonometry.

First, calculate the force of gravity acting on the block, which is given by F = mg, where m is the mass of the block and g is the acceleration due to gravity. Then, use the angle of inclination and the weight of the block to find the normal force, which is equal in magnitude to the force of gravity acting perpendicular to the inclined plane.

Next, use the formula for the frictional force, Ff = μN, where μ is the coefficient of friction and N is the normal force, to find the magnitude of the frictional force acting on the block.

Finally, use the equation W = Fd to find the rate at which the frictional force is doing work on the block. You can also use W = ΔKE to find the work done by the frictional force, where ΔKE is the change in kinetic energy of the block. Since the block is moving at a constant speed, the change in kinetic energy is zero, so the work done by the frictional force is also zero. This means that the rate at which the frictional force is doing work on the block is also zero.

In summary, the frictional force is doing no work on the block as it slides down the inclined plane at a constant speed. This is because the kinetic energy of the block remains constant and there is no change in the potential energy of the block.