Question

A \[8.0\,\text{kg}\] box is released from rest at a height \[y_0 =0.25\,\text m\] on a frictionless ramp. The box slides from the ramp onto a rough horizontal surface. The box slides \[2.0\,\text m\] horizontally until it stops.

At the left side is a box labeled m on a ramp that slopes down and to the right. At the bottom of the ramp is a rough horizontal surface. A second box is to the right side of the diagram. An arrow points from the box on the left to the box on the right by flowing the ramp and level surface. A black arrow points rightwards along the horizontal surface to the box on the right and is labeled d.
At the left side is a box labeled m on a ramp that slopes down and to the right. At the bottom of the ramp is a rough horizontal surface. A second box is to the right side of the diagram. An arrow points from the box on the left to the box on the right by flowing the ramp and level surface. A black arrow points rightwards along the horizontal surface to the box on the right and is labeled d.
What is the friction coefficient of the horizontal surface?
Round answer to two significant digits

Answer 1

To find the friction coefficient of the horizontal surface, we need to use the given information about the box sliding down the ramp and stopping after sliding horizontally. The frictional force can be determined using the equation: F_friction = mu * F_normal. The coefficient of friction is found to be 1.00.

Step-by-step explanation:

To find the friction coefficient of the horizontal surface, we need to use the given information about the box sliding down the ramp and stopping after sliding horizontally. The frictional force can be determined using the equation:

F_friction = µ * F_normal

where µ is the coefficient of friction and F_normal is the normal force exerted on the box. The normal force is equal to the weight of the box, so:

F_normal = m * g

where m is the mass of the box and g is the acceleration due to gravity. We can substitute these values into the equation and solve for the coefficient of friction:

µ = F_friction / F_normal = F_friction / (m * g)

Plugging in the given values, we have:

µ = (8.0 kg * 9.8 m/s^2) / (8.0 kg * 9.8 m/s^2) = 1.00

Therefore, the friction coefficient of the horizontal surface is 1.00.