Question

A box is sliding up an incline that makes an angle of 13.7° with respect to the horizontal. The coefficient of kinetic friction between the box and the surface of the incline is 0.179. The initial speed of the box at the bottom of the incline is 2.29 m/s. How far does the box travel along the incline before coming to rest?

Answer 1

To find the distance traveled by the box along the incline before coming to rest, we can calculate the acceleration and use the equation of motion.

Step-by-step explanation:

To find how far the box travels along the incline before coming to rest, we can calculate the acceleration of the box using the formula:

acceleration = (g * sin(angle)) - (coeff_friction * g * cos(angle))

where g is the acceleration due to gravity, angle is the incline angle, and coeff_friction is the coefficient of kinetic friction. Once we have the acceleration, we can use the equation of motion vf^2 = vi^2 + 2ad to find the distance traveled (d). Rearranging the equation, we get:

d = (vf^2 - vi^2) / (2 * acceleration)

where vf is the final velocity (0 m/s) and vi is the initial velocity (2.29 m/s).

Plugging the given values into these equations will give us the distance traveled by the box along the incline before coming to rest.