A 68.0 kg crate rests on a level floor at a shipping dock. The coefficients of static and kinetic friction are 0.700 and 0.450, respectively.
(a) What horizontal pushing force is required to just start the crate moving?
To find the horizontal pushing force required to start the crate moving, we need to consider the coefficient of static friction. The formula for calculating the force of static friction is:
Fs = μs * N
Where:
Fs is the force of static friction
μs is the coefficient of static friction
N is the normal force acting on the crate
The normal force, N, is equal to the weight of the crate, which can be calculated as:
N = m * g
Where:
m is the mass of the crate (68.0 kg)
g is the acceleration due to gravity (9.8 m/s^2)
Substituting the values, we can find the normal force:
N = (68.0 kg) * (9.8 m/s^2)
N = 666.4 N
Now, we can calculate the force of static friction:
Fs = (0.700) * (666.4 N)
Fs = 466.48 N
Therefore, the horizontal pushing force required to start the crate moving is approximately 466.48 N.