A 50.9-kg crate rests on a level floor at a shipping dock. The coefficients of static and kinetic friction are 0.526 and 0.311, respectively. What horizontal pushing force is required to (a) just start the crate moving and (b) slide the crate across the dock at a constant speed?
M*g = 50.9 * 9.8 = 499 N. = Wt. of crate.
= Normal(Fn).
Fs = u*Fn = 0.526 * 499 = 264 N. = Force of static friction.
Fk = 0.311 * 499 = 155.2 N. = Force of kinetic friction.
a. (Fap-Fs) = M*a.
Fap-264 = M*0 = 0.
Fap = 264 N. = Fore applied.
b. (Fap-Fk) = M*a.
Fap-155.2 = M*0 = 0.
Fap = 155.2 N.
To determine the horizontal pushing force required to start the crate moving and to slide it across the dock at a constant speed, we need to consider the forces acting on the crate.
(a) Just starting the crate moving:
To calculate the horizontal pushing force required to start the crate moving, we need to compare the force of static friction with the maximum force of static friction.
1. The force of static friction (Fs) can be calculated using the formula: Fs = μs * N,
where μs is the coefficient of static friction and N is the normal force.
2. The normal force (N) is equal to the weight of the crate, which can be calculated as: N = m * g,
where m is the mass of the crate and g is the acceleration due to gravity (approximately 9.8 m/s²).
3. Substitute the values into the equation to calculate the force of static friction.
Fs = μs * N
= μs * (m * g)
4. Plug in the given values:
mass of crate (m) = 50.9 kg
coefficient of static friction (μs) = 0.526
acceleration due to gravity (g) = 9.8 m/s²
(b) Sliding the crate across the dock at a constant speed:
To calculate the horizontal pushing force required to slide the crate at a constant speed, we need to find the force of kinetic friction.
1. The force of kinetic friction (Fk) is given by: Fk = μk * N,
where μk is the coefficient of kinetic friction.
2. Calculate the normal force (N) as done in step 2 of part (a).
3. Substitute the values into the equation to calculate the force of kinetic friction.
Fk = μk * N
= μk * (m * g)
4. Plug in the given values:
mass of crate (m) = 50.9 kg
coefficient of kinetic friction (μk) = 0.311
acceleration due to gravity (g) = 9.8 m/s²
I'll now calculate the forces for you.