A 170-kg merry-go-round in the shape of a uniform, solid, horizontal disk of rad

Question

A 170-kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius 1.50 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. What constant force would have to be exerted on the rope to bring the merry-go-round from rest to an angular speed of 0.800 rev/s in 2.00 s? (State the magnitude of the force.) A horizontal 810-N merry-go-round of radius 1.40 m is started from rest by a constant horizontal force of 50 N applied tangentially to the merry-go-round. Find the kinetic energy of the merry-go-round after 5.0 s. (Assume it is a solid cylinder.) Two forces are acting on an object. Which of the following statements is correct? The object is in equilibrium if the net force and the net torque on the object are both zero. The object cannot be in equilibrium because more than one force acts on it. The object is in equilibrium if the net torque on the object is zero. The object is in equilibrium if the forces act at the same point on the object. The object is in equilibrium if the forces are equal in magnitude and opposite in direction. A block slides down a frictionless ramp, while a hollow sphere and a solid ball roll without slipping down a second ramp with the same height and slope. Rank the arrival times at the bottom from shortest to longest.

Explanation / Answer

w = 810 N ; r = 1.4 m ; F = 50 N ; t = 5 s

moment of inertia of merry go round will be:

I = 1/2 m r^2 = 1/2 (w/g)r^2

I = 0.5 x 810/9.8 x 1.4^2 = 81 kg-m^2

torque = I alpha = F x r

alpha = 50 x 1.4/81 = 0.86 rad/s^2

from eqn in circular motion

w = wo + alphat = 0 + 0.86 x 5 = 4.3 rad/s

KE = 1/2 I v^2

KE = 0.5 x 81 x 4.3^2 = 748.85 J

HEnce, KE = 745.85 J

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.