Question

A 305-N solid sphere of radius 0.4 m is released from rest and rolls without slipping from the top to the bottom of a ramp of length 5 m that is inclined at an angle of 25 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 Energy (KE) Translational Kinetic Energy (KE) Both KE and KE, GPE, KE, and KE, b. What type(s) of energy does the object have when it reaches the bottom of the ramp? Gravitational Potential Energy (GPE) Rotational Kinetic Energy (KE) Translational Kinetic Enemy (KE) Both KE, and KE, GPE, KE, and KE, c. Find the moment of inertia of the object. I= unit d. Find the translational speed of the center of mass of the object when it reaches the bottom of the ramp. Ve unit e. Find the angular speed of the object when it reaches the bottom of the ramp. = unit

Answer 1

a)

gravitational potential energy

b)

both rotational and translational energy

c)

I = (2/5) m r^2 = ( 2/5) (305 / 9.8)* 0.4^2 = 2 kgm^2

d)

using conservation of energy

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

mgh = 0.5 m v^2 + 0.5 (2/5) m r^2 * v^2/r^2

9.8*5 sin 25 = 0.7 v^2

v = 5.439 m/s

rotational velocity

w = v/r = 5.439 / 0.4 = 13.6 rad/s

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