A box is placed on a conveyor belt that moves with a constant speed of 1.05 m/s . The coefficient of kinetic friction between the box and the belt is 0.800.

How much time does it take for the box to stop sliding relative to the belt?

How far does the box move in this time?

To find the time it takes for the box to stop sliding relative to the belt, we can use the concept of acceleration. When the box stops sliding, the net force acting on it will be zero. The net force is given by the equation:

net force = frictional force

The frictional force can be calculated using the equation:

frictional force = coefficient of kinetic friction × normal force

The normal force is the force exerted by the belt on the box in the vertical direction and is equal to the weight of the box, which can be calculated using:

weight = mass × gravitational acceleration

First, let's find the normal force:

normal force = weight = mass × gravitational acceleration

Next, let's calculate the frictional force:

frictional force = coefficient of kinetic friction × normal force

Since the net force should be zero when the box stops sliding, we can set the frictional force equal to zero and solve for the mass of the box:

0 = coefficient of kinetic friction × (mass × gravitational acceleration)

Solving for the mass of the box gives us:

mass = 0 / (coefficient of kinetic friction × gravitational acceleration)

Once we have the mass of the box, we can calculate the acceleration using Newton's second law of motion:

net force = mass × acceleration

Since the net force is zero when the box stops sliding, the acceleration will be zero as well. Therefore, the time it takes for the box to stop sliding relative to the belt is infinite.

Now let's calculate the distance the box moves in this time. Since the box moves at a constant speed of 1.05 m/s, the distance it moves can be calculated using the equation:

distance = speed × time

Since the time is infinite, the distance the box moves will also be infinite.

Therefore, the box will never stop sliding relative to the belt and will move an infinite distance.