A student of mass m = 54 kg wants to measure the mass of a playground merry-go-r
ID: 1971699 • Letter: A
Question
A student of mass m = 54 kg wants to measure the mass of a playground merry-go-round, which consists of a solid metal disk of radius R = 1.5 m that is mounted in a horizontal position on a low-friction axle. She tries an experiment: She runs with speed v = 6.9 m/s toward the outer rim of the merry-go-round and jumps on to the outer rim, as shown in the figure. The merry-go-round is initially at rest before the student jumps on and rotates at 1.3 rad/s immediately after she jumps on. You may assume that the student's mass is concentrated at a point.(a) What is the mass of the merry-go-round?
(b) If it takes 38 s for the merry-go-round to come to a stop after the student has jumped on, what is the average torque due to friction in the axle?
(c) How many times does the merry-go-round rotate before it stops, assuming that the torque due to friction is constant? how many revolutions?
Will give an A+ rating for the correct answers. Thanks.
Explanation / Answer
(a) Mom. of Inertia for disc roundabout .. Ir = ½MR² .. (M = roundabout mass) For girl on the roundabout .. Ig = mR² .. (m = girl's mass) Total Mom. of Inertia .. It = R²(M/2 + m) Total angular mom. (It.?) gained from girl's angular momentum as she lands on roundabout (mvR) mvR = R²(M/2 + m).? M = 2([mv/R?] - m) = 2([54*6.2 / 1.50*1.30] - 54) .. .. M = 472.32 kg (b) Rotational distance to stop given by .. ?(rad) = (Av. rot. vel. in rad/s) * time (s) ? = 1.30/2 * 37 = 24.05 rad Frictional torque = T (Nm) Work done against friction = T? = KE lost = ½ (It)?² T? = ½ (It)?² T = ½ ([R²[M/2 + m])(1.30)² = ..... 215.6 / 30.49 .. .. T = 22.9 Nm (c) No. of revs = ?/2p = 24.05 / 2p ..... = 3.82 revs.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.