Find the coefficient of friction between a 73 kg cubic box and a hardwood floor if a total of 236 N is required to start the box moving.

To determine the coefficient of friction between the box and the hardwood floor, we start by using the frictional force equation, which is defined as:

Frictional Force = Coefficient of Friction × Normal Force

In this scenario, the frictional force is the total force required to get the box moving, which is given as 236 N. The normal force is the weight of the box, calculated by multiplying its mass by the acceleration due to gravity. Assuming that the acceleration due to gravity is approximately 9.81 m/s², the normal force can be calculated as follows:

Normal Force = mass × gravity = 73 kg × 9.81 m/s² ≈ 716.93 N

Now, we can substitute these values into the frictional force equation:

236 N = Coefficient of Friction × 716.93 N

To find the coefficient of friction, we rearrange the equation:

Coefficient of Friction = Frictional Force / Normal Force = 236 N / 716.93 N ≈ 0.329

This result rounds to approximately 0.33, which matches the answer provided. The coefficient of friction quantifies the relationship between the frictional force resisting the motion and the normal