Physics 1A Training Set Cycle 3 #3 UCSD Physics

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1 Work by Dissipative Forces In this training set, you re going to consider dissipative energy loss in a system, by calculating the change in total energy done by dissipative work (vectors in bold): E final E initial = ΔE = Δ(KE + PE) = W dissipative = F dissipative Δr where F dissipative are dissipative forces such as friction or drag force. Part 1: Setting up the Problem ( Friction) Analyze one (1) of the following problems using steps from the General Procedure for Solving Problems Using Energy. The first case has been done as an example. (a) A 4.0 kg box is placed on an inclined plane of length L = 3.5 m tilted by θ = 30º and released from rest. The coefficient of kinetic friction between the box and plane surface is µ k = Find the speed of the box at the bottom of the incline. Knowns: m = 4.0 kg; Δr = 3.5 m; θ = 30º; µ k = 0.25; v initial = 0 m/s Target: v final Predictions: box will accelerate down the incline, but lose energy to friction Forces: weight (conservative), normal (constraint), friction (dissipative) Force diagram, direction of motion & coordinate system: 0 J 2 ½ mv f mgh = mglsinθ 0 J mglsinθ 2 ½ mv f Dissipative work: W diss = F f Δr = µ k F N L = µ k mglcosθ (last substitution assuming ΣF y = ma y = 0) Change in energy and solve for unknown(s): ΔE = E final - E initial = ½ mv f 2 mglsinθ = µ k mglcosθ => v f = [2gL(sinθ µ k cosθ)] 1/2 = [2(9.8 m/s 2 )(3.5 m)(sin30º-0.25cos30º)] 1/2 = 4.4 m/s 1

2 (b) A 0.40 kg block is at rest on plane sloped by 15º, held up by friction. It is struck on its left side in such a way as to give it an initial velocity of 1.5 m/s down the plane. However, it slows to a stop in only 0.90 m. What is the coefficient of kinetic friction between the block and plane surfaces? Knowns: Target: Predictions: Force diagram, direction of motion & coordinate system: Dissipative work: Change in energy and solve for unknown(s): 2

3 (c) A 2.0 kg block on a horizontal table is connected to a spring with spring constant k = 150 N/m, which is itself attached to a wall. The spring is compressed by 0.20 m and released from rest. The coefficient of kinetic friction between block and table surfaces is How fast is the block moving when the spring comes back to its rest length? Knowns: Target: Predictions: Force diagram, direction of motion & coordinate system: Dissipative work: Change in energy and solve for unknown(s): 3

4 Part 2: Lost Energy In many cases, it is easier to calculate the work done by friction forces by simply determining the energy lost. For each of the following cases, compute the energy lost and the magnitude of the average dissipative force (F d = ΔE/Δr) by computing and comparing the initial and final total energies. Note that (a) is relevant to your cycle project. (a) A10 gram water drop falls down a 30 m waterfall**, reaching a terminal velocity of about 10 m/s. Energy lost: Average dissipative force: Where did the dissipated energy go? ** You might consider calculating your answer using your team s waterfall parameters. 4

5 (b) A rubber ball of mass 0.10 kg is released from rest 1.2 m above the floor. On its first bounce it comes straight back up to reach a maximum height of 0.95 m. Energy lost: Average dissipative force: Where did the dissipated energy go? 5

6 (c) Riding your bicycle at a constant speed of 8.0 m/s, you approach a hill sloping down at 25º with respecte to horizontal. You decide to simply coast down the 35 m slope without pedaling or braking to see how fast you can go. At the bottom, your speedometer says you are going 15 m/s. Assume a total mass of person + bicycle of 80 kg. Energy lost: Average dissipative force: Where did the dissipated energy go? 6