A mass of 17 kg lies on a horizontal surface with a coefficient of static friction of 0.54 and a coefficient of kinetic friction of 0.22. If a force, F, is applied parallel to the surface (+x direction if you prefer), what is the magnitude that F needs to be to begin to move the object in Newtons?

To calculate the magnitude of the force, F, needed to begin moving the object, we need to consider the maximum static friction. The formula for static friction is:

Fs = μs * N

where Fs is the magnitude of the static friction force, μs is the coefficient of static friction, and N is the normal force.

The normal force, N, is equal to the weight of the object, which can be calculated using the formula:

N = mg

where m is the mass of the object and g is the acceleration due to gravity (9.8 m/s^2).

In this case, the mass of the object is given as 17 kg. So, the normal force is:

N = 17 kg * 9.8 m/s^2 = 166.6 N

Now we can calculate the maximum static friction force using the coefficient of static friction:

Fs = μs * N = 0.54 * 166.6 N = 89.96 N

To begin moving the object, the magnitude of the force, F, needs to be greater than the maximum static friction force. Therefore, the magnitude of F needs to be slightly larger than 89.96 N.

Note: It's important to consider the direction of the force. Since the force is applied parallel to the surface in the positive x-direction, it will be in the same direction as the motion and will help overcome static friction.