Answer :
Final answer:
The force of static friction acting on the luggage is equal to the force applied, which is 77 N. Since the applied force does not exceed the maximum static friction, the luggage remains stationary.
Explanation:
The force of static friction acting on the luggage can be calculated using the coefficient of static friction and the normal force exerted by the luggage onto the floor. The normal force for the luggage can be assumed to be equal to its weight, which is the mass of the luggage multiplied by the acceleration due to gravity (9.8 m/s²). Given a mass of 23 kg, the normal force (N) is:
N = mass × gravity = 23 kg × 9.8 m/s² = 225.4 N
With a coefficient of static friction (µs) of 0.8, the force of static friction (fs) is:
fs = µs × N = 0.8 × 225.4 N = 180.32 N
Since the force applied (77 N) is less than the maximum static friction, the luggage does not move. Therefore, the force of static friction acting on the luggage is equal to the applied force, 77 N, which is option B.
