Sanding block weighs 2.0 N and is pushed with a force of 3.0 N at an angle of 30.0 degrees with respect to the vertical, and angled toward the wall. Moves straight up the wall at a constant speed. What is the coefficient of kinetic friction between the wall and the block?
With an applied vertical force component of 3 cos 30 = 2.598 N, and a weight of 2.0 N, the friction force (downward on the block) must be 0.598 N
The force byt the block applied normal to the wall is 3.0 sin 30 = 1.50 N
The coefficient of kinetic friction of the sandpaper block is
0.598/1.50 = 0.40
To find the coefficient of kinetic friction between the wall and the block, we need to first understand the forces acting on the block.
In this scenario, the block is moving straight up the wall at a constant speed, which means the net force acting on the block must be zero. Since the block is pushed at an angle of 30 degrees with respect to the vertical, we can break down the forces into their vertical and horizontal components.
The vertical forces acting on the block are gravity (mg), pointing downwards, and the normal force (N), pointing upwards. The normal force is equal to the weight of the block when in equilibrium, so N = mg. Since the block is moving up at a constant speed, the vertical forces are balanced, and N = mg = 2.0 N.
The horizontal forces acting on the block are the force pushing the block (Fp) and the force of friction (Ff). The force pushing the block can be broken down into its horizontal and vertical components using the given angle of 30 degrees. The horizontal component is Fp * cos(30), and the vertical component is Fp * sin(30). Since the block is moving horizontally at a constant speed, the net horizontal force is zero. Therefore, Fp * cos(30) = Ff.
The force of friction can be determined using the equation Ff = μ * N, where μ is the coefficient of kinetic friction. Substituting the value for N, we have Fp * cos(30) = μ * mg.
Now we can solve for the coefficient of kinetic friction. Plugging in the given values:
3.0 N * cos(30) = μ * 2.0 N * 9.8 m/s^2
Simplifying the equation:
1.5 N = μ * 19.6 N
Dividing both sides by 19.6 N:
μ = 1.5 N / 19.6 N
Calculating:
μ ≈ 0.08
Therefore, the coefficient of kinetic friction between the wall and the block is approximately 0.08.