A dockworker loading crates on a ship finds that a 25-kg crate, initially at rest on a horizontal surface, requires a 70-N horizontal force to set it in motion. However, after the crate is in motion, a horizontal force of 54 N is required to keep it moving with a constant speed. Find the coefficients of static and kinetic friction between crate and floor.
static friction - ??
kinetic friction - ???
I will be happy to check your work.
To find the coefficients of static and kinetic friction between the crate and the floor, we can use the information provided in the problem.
1. Let's start by finding the coefficient of static friction (μs):
- The force required to set the crate in motion is the maximum static friction force (fs).
- According to Newton's first law of motion, the force needed to set an object in motion is equal to the product of the object's mass (m) and its acceleration (a) - fs = m*a.
- In this case, the mass of the crate (m) is given as 25 kg.
- We know that the force applied to set it in motion is 70 N.
- Hence, fs = 70 N.
- Therefore, fs = μs * normal force (N).
- The normal force (N) is the force exerted by the surface perpendicular to the object's weight. Since the crate is on a horizontal surface, the normal force is equal to the weight of the crate.
- We can calculate the weight of the crate using the formula W = m*g, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
- Weight of the crate (W) = 25 kg * 9.8 m/s^2 = 245 N.
- Substituting the values, 70 N = μs * 245 N.
- Solving for μs: μs = 70 N / 245 N = 0.286.
Therefore, the coefficient of static friction (μs) between the crate and the floor is 0.286.
2. Now, let's find the coefficient of kinetic friction (μk):
- Once the crate is in motion, the force required to keep it moving at a constant speed is the kinetic friction force (fk).
- According to Newton's first law of motion, the force needed to keep an object moving at a constant speed is equal to the product of the object's mass (m) and its acceleration (a) - fk = m*a.
- In this case, the mass of the crate (m) is still 25 kg.
- We know that the force needed to keep it moving is 54 N.
- Hence, fk = 54 N.
- Similar to static friction, fk = μk * normal force (N).
- Since the crate is already in motion, the normal force remains the same (245 N).
- Substituting the values, 54 N = μk * 245 N.
- Solving for μk: μk = 54 N / 245 N = 0.22.
Therefore, the coefficient of kinetic friction (μk) between the crate and the floor is 0.22.
To summarize:
- Coefficient of static friction (μs) = 0.286.
- Coefficient of kinetic friction (μk) = 0.22.