1. A wheel of mass 0.47 kg and radius 48 cm is spinning with an angular velocity
ID: 3901187 • Letter: 1
Question
1. A wheel of mass 0.47 kg and radius 48 cm is spinning with an angular velocity of 17 rad/s. You then push your hand against the edge of the wheel, exerting a force F on the wheel as shown in the figure below. If the wheel comes to a stop after traveling 1/4 of a turn, what is F?
2.An automobile wheel has a mass of 15 kg and a diameter of 0.39 m. What is the total kinetic energy of one wheel when the car is traveling at 11 m/s? (Assume the mass is uniformly distributed throughout the wheel.)
3.For the system of two crates and a pulley in the figure below, what fraction of the total kinetic energy resides in the pulley? (Assume m1 = 18 kg, m2 = 10 kg and mpulley = 7 kg.)
=
4. A sphere rolls down the loop-the-loop track shown in the figure below, starting from rest at a height h above the bottom. The ball travels around the inside of the circular portion of the track
5.A pencil (mass 8.9 g and length 17 cm) is initially balanced so that it is sitting vertically on a flat table as shown in the figure below. If the pencil then falls, what is its angular velocity just before it strikes the tabletop? Assume the mass of the pencil is distributed uniformly and the end of the pencil in contact with the table does not slip.
Explanation / Answer
5.
mass 8.9 g and length 17 cm
we use methods of conservation of energy to solve for this
one the pencil is upright, it has potential energy of mgL where m is the mass of the pencil and L its length
when it falls, just before it hits the table all the PE has converted to KE; the pencil has both translational and rotational KE:
KE=1/2 I w^2 + 1/2 mv^2
I=moment of inertia = 1/3 mL^2 for a rod pivoted at one end
w=angular velocity
v=linear velocity and is related to angular velocity through v= wL
so we have
PE at beginning = KE at end
mgL = 1/2 (1/3 mL^2) w^2 + 1/2 m(w^2 L^2)
cancel through the m's:
gL = 2/3 L^2 w^2
w=sqrt[3g/2L]
for L= 0.0089kg, w=sqrt[3x9.8/0.17]=13.1507rad/s
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