You pull with a force of 255 N on a piece of luggage of mass 68 kg, but it does not move. If the coefficient of friction between the luggage and the floor is 0.7, what is the force of static friction acting on the luggage?

The force of static friction acting on the luggage = 255 N

Explanation:

Applied force = 255 N

mass of luggage=68 kg

coefficient of friction = μ=0.7

Normal force=N = mg

N = 68 (9.8) = 666.4 N

now the force of friction is given by

Ff = μN

Ff=0.7 (666.4)

Ff=466.5 N which is greater than the applied force.

When the applied force is less than the force of friction, in that case

force of friction = applied force

Thus the force of station friction acting on the luggage = 255 N

the other guy was right, the answer is 255