A painter is pressing a 125g paint pad against the ceiling with a force of 8.3 N at an angle of 30° from the vertical. The pad moves at a constant velocity. What is the coefficient of friction between the pad and ceiling?
To find the coefficient of friction between the pad and the ceiling, we need to analyze the forces acting on the paint pad.
First, let's break down the force of 8.3 N into its vertical and horizontal components:
Vertical Component: Fv = F * sin(30°)
Horizontal Component: Fh = F * cos(30°)
Where F is the force of 8.3 N.
Since the paint pad is moving at a constant velocity, we know that the net force acting on it is zero. Therefore, the force of friction between the pad and the ceiling must be equal in magnitude and opposite in direction to the horizontal component of the applied force.
So the force of friction can be given as:
Ffriction = -Fh
Now, we can use the equation for the force of friction:
Ffriction = μ * N
Where μ is the coefficient of friction and N is the normal force. The normal force is equal to the weight of the paint pad, which can be calculated as:
N = m * g
Where m is the mass of the paint pad (125 g) and g is the acceleration due to gravity (9.8 m/s²).
Now, let's calculate the normal force and the force of friction:
N = 0.125 kg * 9.8 m/s² = 1.225 N
Ffriction = -Fh = -F * cos(30°) = -8.3 N * cos(30°) ≈ -7.180 N
Now, equating the force of friction and the equation for the force of friction, we have:
-7.180 N = μ * 1.225 N
Simplifying the equation, we find:
μ = -7.180 N / 1.225 N ≈ -5.87
The negative sign indicates that the coefficient of friction is in the opposite direction of the applied force. However, since the coefficient of friction cannot be negative, we discard the negative sign, resulting in:
μ ≈ 5.87
Therefore, the coefficient of friction between the pad and the ceiling is approximately 5.87 (without the negative sign).