A dockworker loading crates on a ship finds that a 24 kg crate, initially at rest on a horizontal surface, requires a 79 N horizontal force to set it in motion. However, after the crate is in motion, a horizontal force of 57 N is required to keep it moving with a constant speed. Find the coefficients of static and kinetic friction between crate and floor.
The initial force it takes to move the crate is given by μs*mg
where μs is the coefficient of static friction.
Similarly, the coefficient of kinetic friction can be calculated from the force it takes to maintain motion.
Post for an answer check if you wish.
I try to looking for this answer but now I think I am a person should answer this question ^^. Ok
Sum F = ma ( because it get loading the crates )
Fp - F(fr) = ma
Fp = ma + F(fr)
Fp = ma + u(k) mg
=> u(k) = (Fp - ma) / mg ( with ma is 0 )
so u(k) = 57/ ( 24*9.8) ( because kenetic friction always moving )
The u(s) you guys can do the same thing , just replace another force number to the equation.
To find the coefficients of static and kinetic friction between the crate and the floor, we need to analyze the forces acting on the crate and apply Newton's laws of motion.
Let's break down the problem step by step:
Step 1: Determine the force required to set the crate in motion.
- The force required to set the crate in motion is the maximum static friction force (fs_max) acting on the crate.
- According to Newton's first law of motion, an object remains at rest until a net force acts on it.
- The applied force to set the crate in motion is equal to fs_max.
- Therefore, fs_max = 79 N.
Step 2: Determine the coefficient of static friction (μs).
- The coefficient of static friction (μs) relates to the maximum static friction force (fs_max).
- fs_max = μs * (normal force).
- The normal force (N) is the force exerted by the surface on the crate, perpendicular to the surface.
- In this case, the crate is on a horizontal surface, so the normal force is equal to the weight of the crate (mg), where m is the mass of the crate and g is the acceleration due to gravity (9.8 m/s²).
- Using the given mass (m = 24 kg), we can calculate the normal force (N = mg = 24 kg * 9.8 m/s²).
- Substitute the value of the normal force into the equation of static friction force: fs_max = μs * (N).
- Substitute the known value of fs_max (79 N) and the normal force into the equation to find μs.
Step 3: Determine the force required to keep the crate moving at a constant speed.
- Once the crate is in motion, the force required to keep it moving at a constant speed is equal to the kinetic friction force (fk) acting on the crate.
- In this case, the force required to keep the crate moving is given as 57 N, which is equal to fk.
Step 4: Determine the coefficient of kinetic friction (μk).
- The coefficient of kinetic friction (μk) relates to the kinetic friction force (fk).
- fk = μk * (normal force).
- Substitute the known value of fk (57 N) and the normal force into the equation to find μk.
Let’s calculate the values:
Step 2 (Continued): Calculate the coefficient of static friction (μs).
- fs_max = μs * (N).
- Substitute the known value of fs_max (79 N) and the normal force (N = mg) into the equation to find μs.
Step 3 (Continued): Calculate the coefficient of kinetic friction (μk).
- fk = μk * (N).
- Substitute the known value of fk (57 N) and the normal force (N = mg) into the equation to find μk.
By following these steps and applying the equations, you can find the coefficients of static and kinetic friction between the crate and the floor.