A 20 kg mass is at rest on a level surface where the coefficient of static friction is 0.68.
a) How much force will it take to get the mass to move.
b) If a horizontal applied force of 72 Newtons is acting on the mass, how much friction is acting?
To answer these questions, we need to use the concept of static friction and the equation for calculating frictional force.
a) The force required to get the mass to move is equal to the maximum force of static friction. The formula to calculate static friction is:
Fs = μs * N
where:
Fs = force of static friction
μs = coefficient of static friction
N = normal force
To find the normal force (N), we need to consider that the mass is at rest on a level surface. In this case, the normal force is equal to the weight of the mass, which is given by:
N = m * g
where:
N = normal force
m = mass
g = acceleration due to gravity (approximately 9.8 m/s^2)
Substituting the values, we have:
m = 20 kg
g = 9.8 m/s^2
N = 20 kg * 9.8 m/s^2
N = 196 N
Now we can calculate the force of static friction (Fs):
Fs = μs * N
Fs = 0.68 * 196 N
Fs = 133.28 N
Therefore, it will take 133.28 Newtons of force to get the mass to move.
b) If a horizontal applied force (Fa) of 72 Newtons is acting on the mass, we can find the frictional force (f) using the following equation:
f = Fa - Fs
where:
f = frictional force
Fa = applied force
Fs = force of static friction
Substituting the given values:
Fa = 72 N
Fs = 133.28 N
f = 72 N - 133.28 N
f = -61.28 N
The negative value indicates that the friction force acts in the opposite direction to the applied force. In this case, the frictional force acting on the mass is 61.28 Newtons.