A crate with a mass of 50 kg has a coefficient of static friction with the floor of 0.8 and a coefficient of kinetic friction of 0.25. If it is pushed with a force of 425 N, how long will it take to move it across a 65 meter horizontal floor?
To determine the time it takes to move the crate across the floor, we first need to calculate the net force acting on the crate and then use Newton's second law of motion to find the acceleration. Finally, we can use the equations of motion to find the time it takes to cover the given distance.
1. Calculate the net force: The net force can be calculated by subtracting the force of friction from the applied force. The force of friction is given by the product of the coefficient of static friction and the normal force (which equals the weight of the crate, since it is on a horizontal floor). So, the force of friction is:
Force of friction (f) = coefficient of static friction * Normal force
Normal force = mass * gravitational acceleration
Normal force = 50 kg * 9.8 m/s^2
Force of friction (f) = 0.8 * (50 kg * 9.8 m/s^2)
2. Calculate the net force: Subtract the force of friction from the applied force to get the net force:
Net force (Fnet) = Applied force - Force of friction
Net force (Fnet) = 425 N - Force of friction
3. Calculate the acceleration: Use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
Fnet = mass * acceleration
Acceleration = Fnet / mass
Acceleration = (425 N - Force of friction) / 50 kg
4. Calculate the time: Use one of the equations of motion that relates distance, initial velocity, acceleration, and time. Since the crate starts from rest (initial velocity = 0), we can use the equation:
Distance = (1/2) * acceleration * time^2
By rearranging the equation, we can solve for time:
Time = sqrt((2 * Distance) / acceleration)
Time = sqrt((2 * 65 m) / [(425 N - Force of friction) / 50 kg])
Now, you can substitute the values we found earlier to calculate the time it takes to move the crate across the floor.