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?
weight = normal force = m g = 50.9*9.81 =499 N
so
.526 * 499
and
.311 * 499
To solve this problem, we need to use the concepts of static and kinetic friction.
(a) To find the horizontal pushing force required to just start the crate moving (the force needed to overcome static friction), we can use the following steps:
Step 1: Calculate the maximum static friction force.
Static friction force (F_static) = coefficient of static friction (μ_static) * normal force (N)
The normal force is equal to the weight of the crate, which is given by:
Normal force (N) = mass (m) * acceleration due to gravity (g)
Here, the mass of the crate (m) is given as 50.9 kg and the acceleration due to gravity (g) is approximately 9.8 m/s².
So, N = 50.9 kg * 9.8 m/s²
Step 2: Calculate the maximum static friction force:
F_static = 0.526 * N
Step 3: Determine the minimum horizontal force needed to start the crate moving:
The minimum horizontal force (F_min) required to overcome static friction is the same as the maximum static friction force.
F_min = F_static
(b) To find the horizontal pushing force required to slide the crate across the dock at a constant speed (the force needed to overcome kinetic friction), we can use the following steps:
Step 1: Calculate the kinetic friction force.
Kinetic friction force (F_kinetic) = coefficient of kinetic friction (μ_kinetic) * normal force (N)
Step 2: Determine the horizontal force needed to keep the crate moving at a constant speed.
The horizontal force (F) required to keep the crate moving at a constant speed is equal to the kinetic friction force.
F = F_kinetic
Now that we have the steps, let's calculate the values:
Step 1: Calculate the maximum static friction force (F_static):
N = 50.9 kg * 9.8 m/s² = 498.82 N
F_static = 0.526 * 498.82 N ≈ 261.91 N
Step 2: Determine the minimum horizontal force needed to start the crate moving (F_min):
F_min = F_static = 261.91 N
Now, let's calculate the kinetic friction force (F_kinetic) and horizontal force (F) required to keep the crate moving at a constant speed:
F_kinetic = 0.311 * 498.82 N ≈ 154.94 N
F = F_kinetic = 154.94 N
Therefore, the horizontal pushing force required is:
(a) Just to start the crate moving: F_min ≈ 261.91 N
(b) To slide the crate at a constant speed: F ≈ 154.94 N