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HW 1 Solutions
Equilibrium of a Mobile Conceptual Question
(
Conceptual Question).
The artist Anya
Calderona constructs the mobile shown in the figure.
In the illustrated configuration, the mobile
is perfectly balanced.
If Anya decides to make the star twice as massive, and not
change the length of any crossbar or the location of any
object, what does she have to do with the mass of the smiley
face to keep the mobile in perfect balance? Note that she
may have to change masses of other objects to keep the
entire structure balanced.
Answer
: make it twice as massive.
Test Your Understanding 10.3: RigidBody Rotation about a Moving Axis.
A uniform cylinder rolls up an incline without slipping. As it rolls uphill, its speed decreases.
The surface of the incline and the cylinder are both perfectly rigid.
Which of the forces on the
cylinder exert(s) a torque about the center of the cylinder?
Answer: the friction force.
Since the surface and incline are perfectly rigid, the normal force exerted by the incline on the
cylinder is directed toward the cylinder's center. Hence, this force exerts zero torque about the
center. The weight of the cylinder acts at its center (because the cylinder is uniform), so this
force also exerts zero torque around the center. The friction force acts tangential to the
circumference of the cylinder, so it does exert a torque around the center.
Torque Magnitude Ranking Task.
The wrench in the figure has six forces of equal magnitude.
Rank these forces (A through F) on the basis of the magnitude
of the torque they apply to the wrench, measured about an axis
centered on the bolt.
Rank from largest to smallest. To rank
items as equivalent, overlap them.
We assume that all the forces are of the same magnitude.
The moment arm values (ranked from largest to smallest): D, B
and E, F, A, C.
The moment arm that corresponds to F is greater than that for A because the
angle between the wrench axis and horizontal direction is less than 45
0
.
Net Torque on a Pulley.
The figure below shows two blocks suspended by a cord over a pulley. The mass of block B is
twice the mass of block A, while the mass of the pulley is equal to the mass of block A. The
blocks are let free to move and the cord moves on the pulley without slipping or stretching.
There is no friction in the pulley axle, and the cord's weight can be ignored.
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View Full DocumentThe statement that correctly describes the system shown
in the figure: the angular acceleration of the pulley is
nonzero.
Indeed, block B moves with acceleration down, block A
moves with acceleration up.
Since the cord moves on
the pulley without slipping, the linear speed of the
pulley surface,
v
, increases, and this means that the
angular acceleration is nonzero:
dd
v
dt
dt
r
ω
α
⎛⎞
==
⎜⎟
⎝⎠
,
where
r
is the radius of the pulley.
On the other hand,
this also means that the net torque on the pulley is nonzero:
I
τ
=
where
τ
is the net torque on the pulley,
I
is the pulley’s moment of inertia.
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 Spring '11
 EIns

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