1. The problem statement, all variables and given/known data An electric motor and a rope are used to pull a 10kg crate of car parts up an inclined plane. The crate starts out from rest on the ground and ends up with a speed of "vf" at a height of 4.0m above the ground. The graph provided shows the force exerted on the crate by the motor as it is pulled 10m up the inclined plane. a) How much work is done on the crate by the electric motor from d=0 to d=10? b) 150J of heat energy is produced through friction during the 10m pull. What is the final speed of the crate at d=10m? 2. Relevant equations a) Work= area under the graph Area of a Trapezoid = (1/2)*(a+c)*(b) b) Δ E = Heat 3. The attempt at a solution a) Work = area under the graph W= (1/2)*(a+c)*(b) W= (1/2)*(50+65)*(10) W= 575J b)ΔE= Heat ΔEp + ΔEk = Heat (Epf - Epi) + (Ekf - Eki) = 150J (Epf- 0) + (Ekf - 0) = 150J mghf + (1/2)mvf(squared) = 150J ((10)(9.80)(4.0)) + ((1/2)(m)(vf(squared)) = 150J 392 + ((1/2)(10)(vf(squared)) = 150J this is where I run into the problem, if I try to isolate the vf by moving the 392 to the right side to subtract from the 150J I get a negative number which I will then have to square root which is impossible. I was just wondering whether I was going in the right direction ( for both questions "a" and "b") and if I am how am I supposed to isolate the vf here so that I can get an answer when I square root it?