A dock worker loading crates on a ship
finds that a 18 kg crate, initially at rest on a horizontal surface, requires a 71 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/s
2.
Find the coefficient of static friction between crate and floor.
Answering my own question here, but...
µs (static friction)
Ffs (peak frictional force)
Fn (Normal force -needs to be in Newtons-)
Ffs = µs * Fn
71 = µs * (18 * 9.8)
71 = µs * 176.4
71 / 176.4 = µs * 176.4 / 176.4 (isolates the variable µs)
.4024943311 = µs
replaces 71 with 46 to find µk ( kinetic friction)
Answering my own question here, but...
µs (static friction)
Ffs (peak frictional force)
Fn (Normal force -needs to be in Newtons-)
Ffs = µs * Fn
71 = µs * (18 * 9.8)
71 = µs * 176.4
71 / 176.4 = µs * 176.4 / 176.4 (isolates the variable µs)
.4024943311 = µs
replace 71 with 46 to find µk ( kinetic friction)
To find the coefficient of static friction between the crate and the floor, you can use the following steps:
1. Determine the normal force acting on the crate: The normal force is equal to the weight of the crate, which can be calculated as the mass of the crate multiplied by the acceleration due to gravity. In this case, the crate has a mass of 18 kg, so the normal force is (18 kg)(9.8 m/s^2) = 176.4 N.
2. Calculate the force of static friction: The force of static friction is the force required to set the crate in motion, which in this case is 71 N.
3. Apply Newton's second law: The force of static friction can be determined using Newton's second law, which states that the net force acting on an object is equal to the product of its mass and acceleration. However, in this case, since the crate is not moving, the net force is equal to zero. Therefore, we can set up the equation as follows: 0 = force of static friction - applied force.
4. Solve for the force of static friction: Rearranging the equation, we find that the force of static friction is equal to the applied force. Therefore, the force of static friction is 71 N.
5. Calculate the coefficient of static friction: The coefficient of static friction can be found by dividing the force of static friction by the normal force. In this case, the coefficient of static friction is (71 N) / (176.4 N) = 0.402.
Therefore, the coefficient of static friction between the crate and the floor is approximately 0.402.