The coefficient of kinetic friction between a refrigerator (mass 93 kg) and the floor is 0.12, and the coefficient of static friction is 0.35. If you apply the minimum force needed to get the refrigerator to move, what will the acceleration then be?
To find the acceleration of the refrigerator, we need to determine the net force acting on it. The net force is equal to the force of friction.
The force of friction can be determined by multiplying the coefficient of friction (μ) by the normal force (N). The normal force is the force exerted by a surface to support the weight of an object resting on it.
1. Calculate the normal force:
The normal force (N) is equal to the weight of the refrigerator.
Weight (W) = mass (m) * acceleration due to gravity (g)
Given:
Mass (m) = 93 kg
Acceleration due to gravity (g) = 9.8 m/s²
Substitute the given values into the equation:
W = m * g
W = 93 kg * 9.8 m/s²
Calculate the weight:
W = 911.4 N
Therefore, the normal force is 911.4 N.
2. Calculate the force of friction:
The force of friction (F(friction)) can be calculated using the coefficient of kinetic friction (μk) and the normal force (N).
F(friction) = μk * N
Given:
Coefficient of kinetic friction (μk) = 0.12
Normal force (N) = 911.4 N
Substitute the given values into the equation:
F(friction) = 0.12 * 911.4 N
Calculate the force of friction:
F(friction) = 109.37 N
3. Calculate the acceleration:
Since we are applying the minimum force needed to get the refrigerator moving, the applied force (F(applied)) is equal to the force of friction (F(friction)).
F(applied) = F(friction)
Given:
F(applied) = 109.37 N
Use Newton's second law to find acceleration (a):
F(net) = m * a
The net force (F(net)) is equal to the applied force (F(applied)) since there are no other forces acting on the refrigerator.
F(net) = F(applied)
109.37 N = 93 kg * a
Solve for acceleration (a):
a = 109.37 N / 93 kg
Calculating the acceleration:
a ≈ 1.18 m/s²
Therefore, the acceleration is approximately 1.18 m/s².