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all the questions are in the attachment

 

PHYSICS

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Summer 201

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Homework #

4

Due Friday
July 12, 2013

1. Two blocks A and B of masses mA = 1.00 kg and mB = 2.00 kg on a horizontal, frictionless table head
toward each other with initial speeds vA = 3.00 m/s and vB = 2.00 m/s. A light spring is attached to
block A, so when the two block collide, they compress the spring and bounce off with velocities v′A and
v′B.

(a) Find the final velocities v′A and v
′
B.

(b) What are the velocities of the blocks when the spring reaches its maximum compression.

(c) How much potential energy was stored in the spring at the instant of maximum compression?

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PHYSICS 221
Summer 2013

Homework #4 Due Friday
July 12, 2013

2. Find the center of mass of the following systems:

(a) Three point masses as shown figure (a) below.

(b) Three identical uniform rectangles of sides a and b forming a U-shape as shown in figure (b) below.

figure (a) figure (b)

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PHYSICS 221
Summer 2013
Homework #4 Due Friday
July 12, 2013

3. A uniform metal plate of edge 2

5

cm has a square section of edge 5.0 cm cut out of it as in the figure.

25 cm

5.0 cm

P

(a) Where is the center of gravity of the plate?

(b) What is the moment of Inertia of the plate about an axis per-
pendicular to it’s plane through the low left corner P.

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PHYSICS 221
Summer 2013
Homework #4 Due Friday
July 12, 2013

4. Assume a disk of uniform mass density σ and radius R. A circular hole of radius a is cut off the disk at
distance b from the center as shown in the figure.

R

a

P

b

(a) Where is the center of gravity of the new shape?

(b) What is the moment of Inertia of the new shape about an axis per-
pendicular to it’s plane through the center of the uncut cylinder,
P?

(c) Substitute in answers in (a) and (b) for R = 10.0 cm, a = 2.00 cm
and b =

7

.00 cm.

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PHYSICS 221
Summer 2013
Homework #4 Due Friday
July 12, 2013

5. A solid disk of radius R has a mass density as a function of radial distance:

σ (r) = σ0

(
1 −

r

R

)
(a) Locate the Center of Mass of this object.

(b) Calculate the moment of inertia of the disk about it’s axle. Express the answer it terms of the disk’s
total mass M.

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PHYSICS 221
Summer 2013
Homework #4 Due Friday
July 12, 2013

6

. A cylinder of uniform mass M and radius r is released from point A of height h on a track as shown in the
figure. The end of the track is a circular path of radius R. The cylinder rolls without slipping. Determine
the radial and tangential acceleration of the cylinder at points B, C (90◦ from B on the circular arc) and
D as shown. Express your answers in terms of given variables, M, h, r, R and/or g. Assume h is hig

h

enough that cylinder will make it to point D without falling off.

h
r

A

B

C

D

R
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PHYSICS 221
Summer 2013
Homework #4 Due Friday
July 12, 2013

7. Assume a block is placed on the top of an upside down semi-spherical bowl as shown in the figure. The
block starts to slide without frictions. At what angle θ from the vartical will the block fly off the bowl
surface? Now consider a circular ring instead of the block and the fact it will roll down the surface without
slipping. What will be the value of the angle θ at which the ring will fly off the bowl surface?

R
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PHYSICS 221
Summer 2013
Homework #4 Due Friday
July 12, 2013

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. A flywheel in the shape of a solid cylinder of radius R = 0.60 m and mass M = 15 kg can be brought to
an angular speed of 12 rad/s in 0.60 s by a motor exerting a constant torque. After the motor is turned
off, the flywheel makes 20 revolutions before coming to rest because of frictional forces (assumed to be
constant during rotation). What percentage of the power generated by the motor is used to overcome the
frictional losses?

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