A horizontal force of 28.5 N will just start the motion of a 65 N block. A force of 23 N is needed to keep it moving at a constant velocity. Find the coefficients of static friction and kinetic friction.
To find the coefficients of static and kinetic friction, we need to use the information given about the applied force required to start the motion and to maintain constant velocity.
First, let's consider the force required to start the motion. The applied force of 28.5 N is equal to the maximum force of static friction (F_static_max) between the block and the surface. Therefore, we can write:
F_static_max = 28.5 N
Next, let's consider the force required to maintain constant velocity. The force required to keep the block moving is equal to the force of kinetic friction (F_kinetic) between the block and the surface. Therefore, we can write:
F_kinetic = 23 N
According to the laws of friction, the force of static friction is given by:
F_static = μ_static * N
where μ_static is the coefficient of static friction and N is the normal force. The normal force N is equal to the weight of the block, which is given as 65 N. So we can rewrite the equation as:
F_static_max = μ_static * N
Substituting the given values, we have:
28.5 N = μ_static * 65 N
Simplifying the equation, we find:
μ_static = 28.5 N / 65 N ≈ 0.438
Therefore, the coefficient of static friction (μ_static) is approximately 0.438.
Now, let's calculate the coefficient of kinetic friction (μ_kinetic). The force of kinetic friction is given by:
F_kinetic = μ_kinetic * N
We already know that F_kinetic is equal to 23 N, and N is still equal to 65 N. Substituting these values into the equation, we have:
23 N = μ_kinetic * 65 N
Simplifying the equation, we find:
μ_kinetic = 23 N / 65 N ≈ 0.354
Therefore, the coefficient of kinetic friction (μ_kinetic) is approximately 0.354.
To summarize:
- The coefficient of static friction (μ_static) is approximately 0.438.
- The coefficient of kinetic friction (μ_kinetic) is approximately 0.354.