Question

A box is pushed, released, and is slide up an incline that makes an angle of 15 degrees with respect to the horizontal. The coefficient of friction between the box and the surface is 0.180. The initial speed of the box after the push is 1.50 m/s. How far does the box travel along the incline before coming to rest. Pease show free body diagram, write equations of each component, find the answer, show the substitution, and leave a explanation. Thank you.

Answer 1

balancing forces along perpendicular to inclined plane N = mg cos theta now along the incline net force F = mg sin theta + MN F = m g sin theta + mu m g cos theta applying work - energy principle work done by force = delta k . E Rightarrow - (m g sin theta + mu mg cos theta) times d = 0 - 1/2 m v^2 Rightarrow d = v^2/2 g (sin theta + mu cos theta) = (1.5)^2 /2 times 9.8 times (sin 15 degree + 0.18 cos 15 degree) d = 0.265 m