Static and Kinetic Friction:
A 10 kg crate is at rest on a horizontal table (s =0.8, k =0.4). Then various amounts of horizontal pushing force are applied to it.
a.) The largest pushing force that can be applied before the crate starts moving is of size:
N
b.)-d.) If the pushing force were instead the two amounts shown below, please fill in the rest of the values on the chart below:
horizontal pushing force: friction force: (size only)
(indicate static or kinetic):
net force on crate:
(size only)
acceleration of crate:
(size only)
13 N N, ---Select--- static kinetic N m/s2
115 N N, ---Select--- static kinetic N m/s2
To answer these questions, we need to understand the concepts of static and kinetic friction.
Static friction is the force that keeps an object at rest when an external force is applied to it. It prevents the object from moving initially. Once the external force overcomes the static friction, the object starts to move. Kinetic friction, on the other hand, is the force that opposes the motion of an object when it is already moving.
In this case, the coefficient of static friction (s) is 0.8 and the coefficient of kinetic friction (k) is 0.4. The mass of the crate is given as 10 kg.
(a) To find the largest pushing force that can be applied to the crate before it starts moving, we need to determine the maximum static friction force. The formula for static friction force is:
Static friction force = coefficient of static friction * normal force
Normal force = mass * gravity
where gravity is approximately 9.8 m/s^2.
Calculating the normal force:
Normal force = 10 kg * 9.8 m/s^2 = 98 N
Calculating the maximum static friction force:
Static friction force = 0.8 * 98 N = 78.4 N
Therefore, the largest pushing force that can be applied before the crate starts moving is 78.4 N.
(b) To determine the friction force, net force, and acceleration for each pushing force:
For the 13 N pushing force:
Friction force = Static friction force (as the crate is at rest) = 78.4 N
Friction type = Static friction
Net force on the crate = Pushing force - Friction force = 13 N - 78.4 N = -65.4 N (negative sign indicates opposing direction)
Acceleration of the crate = Net force / mass = (-65.4 N) / 10 kg = -6.54 m/s^2 (negative sign indicates deceleration)
For the 115 N pushing force:
Friction force = Kinetic friction force (as the crate is already moving) = coefficient of kinetic friction * normal force
Friction force = 0.4 * 98 N = 39.2 N
Friction type = Kinetic friction
Net force on the crate = Pushing force - Friction force = 115 N - 39.2 N = 75.8 N
Acceleration of the crate = Net force / mass = 75.8 N / 10 kg = 7.58 m/s^2
The completed chart would be:
horizontal pushing force: friction force: (size only)
(indicate static or kinetic):
net force on crate:
(size only)
acceleration of crate:
(size only)
13 N 78.4 N static -65.4 N -6.54 m/s^2
115 N 39.2 N kinetic 75.8 N 7.58 m/s^2