A dock worker loading crates on a ship finds that a 24 kg crate, initially at rest on a horizontal surface, requires a 64 N horizontal force to set it in motion. However, after the crate is in motion, a horizontal force of 46 N is
required to keep it moving with a constant speed. The acceleration of gravity is 9.8 m/s2 . Find the coefficient of static friction between crate and floor.
Part B: Find the coefficient of kinetic friction.
forcefriction=mu*mg
64=mu*mg
find mu
b) same, f=46
To find the coefficient of static friction between the crate and the floor, we can start by analyzing the forces acting on the crate when it is at rest. Here's how to proceed:
Step 1: Identify the forces acting on the crate.
When the crate is at rest, the only horizontal force acting on it is the applied force of 64 N. There is also the force of gravity acting vertically downward on the crate, but it does not influence the horizontal motion.
Step 2: Calculate the force of static friction.
In order to set the crate in motion, the applied force must overcome the force of static friction between the crate and the floor. Therefore, when the crate is at rest, the force of static friction (Fs) will be equal in magnitude but opposite in direction to the applied force. So, Fs = -64 N.
Step 3: Relate the frictional force to the normal force.
The force of static friction depends on the normal force (Fn), which is the force exerted by the surface on the crate perpendicular to the surface. In this case, the normal force is equal to the weight of the crate, which is given by Fn = mg, where m is the mass of the crate (24 kg) and g is the acceleration due to gravity (9.8 m/s^2). Therefore, Fn = (24 kg)(9.8 m/s^2) = 235.2 N.
Step 4: Calculate the coefficient of static friction.
The coefficient of static friction (μs) is defined as the ratio of the force of static friction to the normal force. Therefore, μs = |Fs| / Fn, since Fs and Fn have opposite directions. Plugging in our values, we have |Fs| = |(-64 N)| = 64 N. Thus, the coefficient of static friction is μs = 64 N / 235.2 N.
Part B: To find the coefficient of kinetic friction (μk), we can use the information given regarding the force required to keep the crate moving at a constant speed. Follow the steps below:
Step 1: Identify the forces acting on the crate when it is in motion.
When the crate is moving with a constant speed, the applied force is equal to the force of kinetic friction (Fk). The force of kinetic friction is what opposes the motion of the crate.
Step 2: Calculate the force of kinetic friction.
Given that the force required to keep the crate moving with a constant speed is 46 N, we can conclude that Fk = 46 N.
Step 3: Calculate the coefficient of kinetic friction.
The coefficient of kinetic friction (μk) is defined as the ratio of the force of kinetic friction to the normal force. Therefore, μk = Fk / Fn. Plugging in our values, we have Fk = 46 N and Fn = 235.2 N. Thus, the coefficient of kinetic friction is μk = 46 N / 235.2 N.
So, the coefficient of static friction between the crate and the floor is approximately 0.273, while the coefficient of kinetic friction is approximately 0.196.