A force of 40 newtons applied horizontally is required to push a 20-kilogram box at constant velocity across the floor. The coefficient of friction between the box and the floor is
2.
To find the coefficient of friction, we first need to find the frictional force acting on the box. We know that the force required to push the box at constant velocity is 40 newtons. This force is equal to the sum of the force of friction and the force required to overcome the box's inertia.
The force required to overcome the box's inertia is given by the equation F = ma, where F is the force, m is the mass, and a is the acceleration. Since the box is moving at constant velocity, the acceleration is zero, so the force required to overcome inertia is also zero.
Therefore, the force of friction is equal to the force required to push the box at constant velocity, which is 40 newtons.
The frictional force is equal to the coefficient of friction (µ) times the normal force (N), which is equal to the weight of the box (mg), where m is the mass and g is the acceleration due to gravity.
Using the given values, the weight of the box is (20 kg)(9.8 m/s^2) = 196 newtons.
Therefore, the frictional force is µ(196 N).
Since the frictional force is 40 newtons, we can set up the equation:
40 N = µ(196 N)
µ = 40 N / 196 N
µ = 0.204
Therefore, the coefficient of friction between the box and the floor is 0.204.