Question

A315-N thin cylindrical shell, or hoop, of radius 0.35 m is released from rest and rolls without slipping from the top to the bottom of a ramp of length 4.5 m that is inclined at an angle of 20 degrees with the horizontal as shown in the figure below a. What type(s) of energy does the object have when it is released? Gravitational Potential Energy (GPE) Rotational Kinetic Frey(KE. Translational Kinetic Energy (K) Both KE, and KE GPE, KE, and KE N S b. What type(s) of energy does the object have when it reaches the bottom of the ramp? Gravitational Potential Energy (GPE) Rotational Kinetic En abona Kinetic Energy E. Both KE, and KE GPE KE and KE c. Find the moment of inertia of the 19 20 unit 2 S S d. Find the translational speed of the center of mass of the object when it reaches the bottom of the ramp. v = - unit mis e. Find the angular speed of the object when it reaches the bottom of the ramp. 00 unit rad's

Answer 1

a)

gravitational potential energy

b)

both rotational and translational energy

c)

I = (0.5) m r^2 = ( 1/2) (315 / 9.8)* 0.35^2 = 1.969 kg m^2

d)

using conservation of energy

mgh = 0.5 m v^2 + 0.5 Iw^2

mgh = 0.5 m v^2 + 0.5 (1/2) m r^2 * v^2/r^2

9.8*4.5 sin 20 = v^2

v = 3.884 m/s

rotational velocity

w = v/r = 3.884 / 0.35 = 11.1 rad/s

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