A 19 kg wooden crate is dragged across the driveway. The coefficient of kinetic friction between the wood and concrete is 0.64.
A. What is the horizontal force needed to drag the crate uniformly?
B. Give a possible value for the coefficient of state friction.
A. (Weight) x (kinetic friction coefficient)
Remember that weight = M g
B. The static coefficient can be any value greater than the kinetic coefficient value. Usually it is 10% to 60% higher
To answer both parts of the question, we need to understand the concepts of kinetic friction and static friction.
Kinetic friction is the force that opposes the motion of an object when it is moving. It can be calculated using the formula:
Frictional force = coefficient of kinetic friction * normal force
where the normal force is the force exerted by the surface on the object perpendicular to it.
Static friction is the force that needs to be overcome to start the motion of an object. It is usually greater than the kinetic friction. Static friction can be calculated using a similar formula:
Frictional force = coefficient of static friction * normal force
Now let's answer the parts of the question:
A. What is the horizontal force needed to drag the crate uniformly?
To find the horizontal force needed to drag the crate uniformly, we need to calculate the kinetic frictional force acting on the crate.
Given:
Mass of the crate (m) = 19 kg
Coefficient of kinetic friction (µk) = 0.64
First, we need to find the normal force acting on the crate. The normal force is equal to the weight of the crate:
Weight of the crate = mass * gravitational acceleration = m * g
where the gravitational acceleration (g) is approximately 9.8 m/s^2.
So, the normal force (N) acting on the crate is: N = m * g
Next, we can calculate the kinetic frictional force using the formula mentioned earlier:
Frictional force = µk * N
Substituting the values we know:
Frictional force = 0.64 * N
Therefore, the horizontal force needed to drag the crate uniformly is equal to the kinetic frictional force.
B. Give a possible value for the coefficient of static friction.
The coefficient of static friction (µs) represents the resistance to start the motion of an object.
Since the coefficient of kinetic friction (µk) is given and is always lower than the coefficient of static friction, a possible value for the coefficient of static friction would be any value that is higher than 0.64. For example, let's assume µs = 0.8.
Note: The coefficient of static friction can vary depending on the surfaces in contact.