A 100 lb block of ice slides down an incline 5.0 ft long and 3.0 ft high. A worker pushes up on the ice parallel to the incline so that it slides down at constant speed. The coefficient of friction between the ice and the incline is 0.10.
Find (a) the force exerted by the worker, (b) the work done by the worker on the block, (c) the work done by gravity on the block, (d) the work done by the surface of the incline on the block, (e) the work done by the resultant force on the block, and (f) the change in kinetic energy of the block.
I solved a and b, and I get them, but I'm stuck conceptually on the last few parts. On c, my biggest issue is that I think I'm confusing this situation to one where a block attached to a string is lowered (i.e. negative work is done on the block.)
Does (d) even matter since it's not the incline pushing the block down it? Or does friction play a part here?
For (e), if Fnet is 0 (since all the forces have to be 0 for there to be constant speed) does that mean this question is irrelevant?
...I can figure (f) out on my own.
I don't want answers, just...some conceptual help on this one.
I'm here to help you understand the concepts behind each part of the problem. Let's break it down step by step:
(a) The force exerted by the worker: Since the ice slides down at a constant speed, the force of friction acting up the incline must balance the component of the worker's force acting down the incline. To find the force exerted by the worker, you can calculate the force of friction using the equation F_friction = μ * N, where μ is the coefficient of friction and N is the normal force. The normal force can be found as the weight of the block (mass * gravity) multiplied by the cosine of the angle of the incline.
(b) The work done by the worker on the block: Work is equal to force multiplied by distance. In this case, you can calculate the work done by the worker by multiplying the force exerted by the worker (which you found in part (a)) by the distance the block slides down the incline.
(c) The work done by gravity on the block: Since the block is moving parallel to the incline, gravity does not do any work on the block in the direction of motion. The work done by gravity is zero.
(d) The work done by the surface of the incline on the block: The incline does not exert a force in the direction of motion of the block, as the force of friction balances the component of the worker's force acting down the incline. So, the work done by the surface of the incline on the block is also zero.
(e) The work done by the resultant force on the block: Since the net force on the block is zero (constant velocity), the work done by the resultant force is zero.
(f) The change in kinetic energy of the block: This can be calculated using the work-energy theorem. Since the net work done on the block is zero, the change in kinetic energy of the block is also zero.
In summary, parts (c), (d), (e), and (f) all have zero values in this specific scenario. The conceptually important part to understand is that when an object is moving with constant speed, the net work done on the object is zero.