Friction increases speed: calculate acceleration caused by friction, calculate the sliding distance.

Friction doesn't always slow things down! In this problem, friction increases the speed of a box. 🧠 Access full flipped physics courses with video lectures and examples at https://www.zakslabphysics.com/ We start with a box dropped on a fast conveyer belt and the box begins to slip. The conveyor belt is sliding under the box to the right, and this causes a rightward kinetic friction force. In this unusual case, we have kinetic friction doing positive work (friction increases speed of the box)! To calculate the acceleration caused by friction, we begin with a force analysis on the box. We compute the weight of the box, mg, and we compute the normal force on the box, n. Since the conveyor is horizontal and there are no other vertical forces tampering with the box, the normal force exactly balances the force of gravity in this problem, so n=mg, and we've got the normal force. In the second part of the problem, we want to calculate the sliding distance before the box locks into place on the conveyor belt. Physically, this just means we want the distance it takes for the box's speed to increase to the same speed as the conveyor belt itself. At this speed, there is no longer any relative velocity between the box and the conveyor, so the box must lock into place on the belt. We calculate the friction force by using f=mu_k*n, and we get the horizontal force of friction that accelerates the box from rest. Plugging into Newton's second law a=F/m, we arrive at the rightward acceleration induced by friction for the box. Now we know the acceleration, the initial velocity and the final velocity, and we can relate to the slipping distance by using the time independent constant acceleration kinematics formula v^2=v_0^2+2a(x-x_0). We solve for x, plug in the known acceleration, known final velocity and known initial velocity, and we've got the slipping distance for a box accelerated using friction!