A 100kg box is pushed along a road with force of 500N. If the box moves with a uniform velocity, the coefficient of friction between the box and the road is

A 100kg box is pushed along a road with force of 500N. If the box moves with a uniform velocity, the coefficient of friction between the box and the road is

Answer Details

To find the coefficient of friction between the box and the road, we need to use the formula for frictional force, which is given by: f_friction = coefficient of friction x normal force.
Since the box is moving with a uniform velocity, we know that the net force acting on the box is zero. The force pushing the box forward is balanced by the force of friction acting in the opposite direction. Therefore, we can set up an equation to find the force of friction acting on the box:
f_push - f_friction = 0
where f_push is the force pushing the box forward, and f_friction is the force of friction acting in the opposite direction.
Substituting the values given in the problem, we get:
500N - f_friction = 0
Solving for f_friction, we get:
f_friction = 500N
Now, we can use the formula for frictional force to find the coefficient of friction:
f_friction = coefficient of friction x normal force
The normal force is the force exerted by the road on the box, which is equal to the weight of the box (since the box is not accelerating):
normal force = weight of box = mg = 100kg x 9.8 m/s^2 = 980N
Substituting this value and the value we found for the force of friction into the formula for frictional force, we get:
500N = coefficient of friction x 980N
Solving for the coefficient of friction, we get:
coefficient of friction = 500N / 980N = 0.51
Therefore, the coefficient of friction between the box and the road is approximately 0.5, which is the fourth option.