Question

A crate resting on a horizontal floor (μₛ=0.83,μₖ=0.24) has a horizontal force F=75 Newtons applied to the right. This applied force is the maximum possible force for which the crate does not begin to slide. If you applied this same force after the crate is already sliding, what would be the resulting acceleration (in meters/second²)?

Answer 1

The maximum force of static friction can be calculated using the formula Fs,max = μsN. The acceleration of the crate once it starts to slide can be calculated using Newton's second law. When P = 180.0 Nî, the maximum force of static friction is 118 N and the resulting acceleration is 0.9833 m/s².

Step-by-step explanation:

The maximum force that can be exerted horizontally on the crate without moving it is equal to the maximum force of static friction. The formula for calculating the maximum force of static friction is given by

Fs,max = μsN

Where Fs,max is the maximum force of static friction, μs is the coefficient of static friction, and N is the normal force. In this case, we need to calculate Fs,max when P = 180.0 Nî:

Fs,max = (0.600)(196 N) = 118 N

Once the crate starts to slip and kinetic friction comes into play, the acceleration can be calculated using Newton's second law:

Fnet = ma

Where Fnet is the net force and a is the acceleration. In this case, the net force is equal to the force of kinetic friction and the mass is 120 kg. Therefore, we can calculate the acceleration (a) when P = 180.0 Nî:

a = / m = 118 N / 120 kg = 0.9833 m/s²