Answer all questions with all the work: 5. One of my colleagues in grad school g

Question

Answer all questions with all the work:

5. One of my colleagues in grad school gave his lab students the following experiment: A ball was rolled down a curving ramp from an initial height h. The ball then rolled across a horizontal Figure 2: Platform for measuring rotational inertia section of the ramp, and shot off the end of the ramp with some horizontal speed v and initial height off the ground H. The ball would travel some horizontal distance r before hitting the ground. The idea behind the lab was that the students could use h and the mass m of the ball to find the initial potential energy, equate this initial energy mgh to the kinetic energy w2 of the ball as it left the table, and find v. From v and H, the students could then use projectile motion methods to predict exactly how far the ball would go before hitting the ground The problem was that the ball consistently hit at about 85% of the "correct" distance. Air resistance and other non-conservative forces were not sufficient to account for this discrepancy. (a) What was my colleague forgetting? Why was there this systematic error? (b) Show that a correct analysis gives an answer for r which is about 85% of the range predicted by the original analysis. 6. A pair of masses (each with mass m) is arranged with a pulley (also of mass m, and radius r) on the frictionless ramp as shown in the figure below. What is the acceleration of this system? 7. The drum on a washing machine starts from rest and accelerates with an angular acceleration of 1.2 rad/s2 as it goes into its final spin cycle. (a) How long does it take to reach its final angular speed of 15 rad/s? (b) Through what angle does it rotate during this acceleration? (c) How far does a point on the rim move during this acceleration, given a drum radius of 0.4 m?

Explanation / Answer

7. (A) wf = wi + alpha t

15 = 0 + 1.2 t

t = 12.5 sec

(B) wf^2 - wi^2 = 2alpha theta

15^2 - 0^2 = 2(1.2)(theta)

theta = 93.75 rad

(C) d = theta r = 37.5 m

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