A dockworker loading crates on a ship finds that a 17-kg crate, initially at rest on a horizontal surface, requires a 70-N horizontal force to set it in motion. However, after the crate is in motion, a horizontal force of 53 N is required to keep it moving with a constant speed. Find the coefficients of static and kinetic friction between crate and floor.
mg = 17*9.81 = 167 N weight
70 = mu (167)
mu = 70/167 static
53 = mu (167)
mu = 53/167 kinetic
To find the coefficients of static and kinetic friction between the crate and the floor, we can use the given information about the forces required to set the crate in motion and to keep it moving at a constant speed.
First, let's define the forces acting on the crate. There are two forces: the applied force (F_applied) and the force of friction (F_friction).
1. Finding the coefficient of static friction (µ_static):
The coefficient of static friction is denoted as µ_static. It represents the friction between two surfaces when there is no relative motion between them. In this case, the force of friction must be equal to the applied force to set the crate in motion. So, we have:
F_applied = F_friction = µ_static * Normal force
The normal force (F_normal) is the force exerted by the surface perpendicular to the weight of the crate. Since the crate is initially at rest, the normal force is equal to the weight of the crate.
Weight of the crate (F_weight) = mass (m) * acceleration due to gravity (g)
F_weight = m * g
Substituting F_weight for F_normal:
F_applied = µ_static * m * g
From the given information, F_applied = 70 N and m = 17 kg, we can solve for µ_static:
70 N = µ_static * 17 kg * 9.8 m/s²
µ_static = 70 N / (17 kg * 9.8 m/s²)
Calculating this gives the value of µ_static.
2. Finding the coefficient of kinetic friction (µ_kinetic):
The coefficient of kinetic friction is denoted as µ_kinetic. It represents the friction between two surfaces when there is relative motion between them. In this case, the force of friction required to keep the crate moving at a constant speed is equal to the applied force. So, we have:
F_applied = F_friction = µ_kinetic * Normal force
Again, we can use the weight of the crate as the normal force. Therefore, we can write:
F_applied = µ_kinetic * m * g
From the given information, F_applied = 53 N and m = 17 kg, we can solve for µ_kinetic:
53 N = µ_kinetic * 17 kg * 9.8 m/s²
µ_kinetic = 53 N / (17 kg * 9.8 m/s²)
Calculating this gives the value of µ_kinetic.
By solving these equations using the given information, we can determine the coefficients of static and kinetic friction between the crate and the floor.