Physics 204A Problem set 10, due 11/6/17 I. A merry-go-round has radius r = 4.0
ID: 1774900 • Letter: P
Question
Physics 204A Problem set 10, due 11/6/17 I. A merry-go-round has radius r = 4.0 m. Bubba attempts to stop the merry-go round by grabbing the edge. He immediately falls down, but still hangs on. The rotational inertia of Bubba and the merry-go-round, together, is 1 20.000 kg m2. The frictional force between Bubba and the ground is Fr = 490 N. If the merry-go-round is spinning with angular velocity w = 0.62 rad/s immediately after Bubba grabs it, how long until it stops? 2. The wheel of a stationary exercise bicycle is in the form of a uniform disk, with mass 7.2 kg and radius 25 cm. The wheel is initially at rest, but a cyclist applies to it a constant torque of 6.0 Nm for 1.5 seconds. How far does the wheel move in that time? (8) 3. An Atwood's machine consists of two masses hanging on either side of a pulley, as shown in figure 1. Derive the equation for the acceleration of this device, assuming that the pulley is in the shape of a disk. Assume friction at the pulley axle is negligible Figure 1: Atwood's Machine with a "real" pulley 4. It's all well and good to be able to integrate simple shapes to find their rotational inertia: but how does one find the all-important rotational inertia of a rubber chicken? They're hard to integrate! Here's one way to measure I experimentally: First, you assemble a low-friction rotating platform, as shown in figure 2. It should have a string and a pulley off to one side, supporting a mass m as shown. The string should be wrapped around the center spindle, which has radius r. Place the rubber chicken on the platform. (Here shown by the grey box M since I can't draw rubber chickens.) Now release the apparatus, and measure how much time t it takes the mass m to fall a distance h. Find an equation for the rotational inertia I of the rubber chicken and platform, in terms of r, h, m, t, and anything else that comes in handy. (If you repeat the experiment without the rubber chicken, you would obtain the rotational inertia of the empty platform, which you could then subtract from your previous result to find the rotational inertia of the rubber chicken alone.) 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 horizontalExplanation / Answer
1. net torque = I alpha
r Ff = I alpha
4 x 490 = (20,000) alpha
alpha = 0.098 rad/s^2
Applying wf = w0 + alpha t
0.62 = 0 + 0.098 t
t = 6.33 sec