A 140 kg stationary crate is pulled by a force of 390 N along a horizontal surface.
a) The coefficient of static friction between crate and surface is s = 0.25. Is the applied
force large enough to begin moving the crate? Use physics calculations to prove that it is.
b) The coefficient of sliding friction between crate and surface is k = 0.17. Find the net
force and the acceleration of the crate once it does move.
To determine if the applied force is enough to begin moving the crate, we need to compare the force of static friction with the applied force.
a) Calculation:
1. The force of static friction (F_static) can be calculated using the formula:
F_static = μs * N
where μs is the coefficient of static friction, and N is the normal force acting on the crate.
2. The normal force (N) can be calculated as the product of the mass (m) of the crate and the acceleration due to gravity (g):
N = m * g
where m = 140 kg and g = 9.8 m/s^2 (approximate acceleration due to gravity).
3. Substitute the given values into the equation to calculate the normal force:
N = 140 kg * 9.8 m/s^2 = 1372 N
4. Substitute the normal force value into the equation for the force of static friction:
F_static = 0.25 * 1372 N = 343 N
5. Compare the force of static friction with the applied force (F_applied = 390 N). If the applied force is greater than the force of static friction, the crate will begin to move.
Therefore, since the applied force of 390 N is greater than the force of static friction of 343 N, the crate will start moving.
b) Once the crate starts moving, the force of friction changes from static friction to kinetic friction.
The net force acting on the crate is given by:
F_net = F_applied - F_friction
1. The force of kinetic friction (F_friction) can be calculated using the formula:
F_friction = μk * N
where μk is the coefficient of kinetic friction.
2. Substitute the given values into the equation to calculate the force of kinetic friction:
F_friction = 0.17 * 1372 N = 232.64 N (approximately)
3. Substitute the force of kinetic friction into the equation for net force:
F_net = 390 N - 232.64 N = 157.36 N (approximately)
4. The acceleration (a) of the crate can be calculated using Newton's second law:
F_net = m * a
5. Substitute the values into the equation to calculate the acceleration:
157.36 N = 140 kg * a
a ≈ 1.12 m/s^2
Therefore, the net force acting on the crate is approximately 157.36 N, and the acceleration of the crate once it starts moving is approximately 1.12 m/s^2.
To determine whether the applied force is large enough to begin moving the crate, we need to compare the force of static friction with the applied force.
a) The force of static friction can be calculated using the formula:
fs = μs * N
Where fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force.
The normal force in this case is 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).
Therefore, N = 140 kg * 9.8 m/s² = 1372 N.
Substituting the values into the formula, we have:
fs = 0.25 * 1372 N = 343 N.
The force of static friction is 343 N.
If the applied force is larger than the force of static friction, the crate will start moving. In this case, the applied force is 390 N, which is larger than the force of static friction. Thus, the applied force is large enough to begin moving the crate.
b) Once the crate starts moving, it experiences kinetic friction. The force of kinetic friction can be calculated using the formula:
fk = μk * N
Where fk is the force of kinetic friction, μk is the coefficient of sliding friction, and N is the normal force (1372 N in this case).
Substituting the values, we have:
fk = 0.17 * 1372 N = 232.24 N.
The force of kinetic friction is 232.24 N.
The net force on the crate is given by the difference between the applied force and the force of kinetic friction:
Fnet = Fa - fk
Substituting the values, we have:
Fnet = 390 N - 232.24 N = 157.76 N.
The net force on the crate is 157.76 N.
The acceleration of the crate can be calculated using Newton's second law:
Fnet = m * a
Where Fnet is the net force and m is the mass of the crate (140 kg in this case).
Substituting the values and rearranging the equation to solve for acceleration, we have:
157.76 N = 140 kg * a
a = 157.76 N / 140 kg
a ≈ 1.13 m/s².
The acceleration of the crate, once it starts moving, is approximately 1.13 m/s².
(a) Normal force, N= 140g N
μs=0.25
frictional force to move crate
= μN
= 0.25*140g
= 343.35
Assuming force of 340N is acting horizontally, crate will move since 390N > 343.35 N
(b) μk=0.17
kinetic frictional force
= μkN
= 0.17*340*9.81
= 233.48 N
Net force causing acceleration
=390-233.48
=156.52 N
Newton's second law: F=ma =>
a=F/m
=156.52/140
=1.12 m/s²