Physics 201 MWF10:20 Fall 1994 (Ford)
Exam III Chapts. 9,10,11,13 in SZY College Physics
Show all your work. Partial credit will be given if earned. Write your
answers in the blanks provided.
(20 pts) 1. A cylinder with radius R = 0.40 m is pivoted on frictionless
bearings about an axis through its center. A rope is wrapped around the
cylinder, and the end of the rope is attached to a block with mass 5 kg.
The system is released from rest, and it is observed that the angular
acceleration of the cylinder is
= 16 rad/s2. Calculate
a) the linear acceleration a of the 5 kg block;
Ans. ________________
b) the tension in the rope, while the system is moving;
Ans. _____________________
c) the moment of inertia I of the cylinder.
Ans. ____________________
(20 pts) 2. A small block on a horizontal frictionless tabletop has a mass of
0.050 kg and is attached to a cord passing through a hole in the tabletop.
The block is originally moving in a circle at a distance of 0.300 m from
the hole, with an angular velocity of 6.0 rad/s. The cord
is pulled from below by a person under the table, shortening the radius of
the circle in which the block moves to 0.200 m. The block may be treated as a
point mass.
a) For an axis through the hole in the tabletop, what is the moment of
inertia of the block when it is 0.300 m from the hole?
Ans. ______________________
b) What is the angular velocity of the block after the radius has become 0.20 m?
Ans. _____________________
c) How much work was done by the person who pulled the cord?
Ans. ___________________
(20 pts) 3. A uniform bar 6.0 m long is attached at one end to a wall by a
frictionless hinge. The bar is held in the position shown by a horizontal
cable. The tension in the horizontal cable is 60 N.
a) For an axis at the hinge, what is the magnitude of the torque produced by
the tension in the cable?
Ans. ___________________
b) What is the weight of the bar?
Ans. ___________________
c) What is the magnitude of the resultant force that the hinge exerts on the
bar?
Ans. __________________
(20 pts) 4. A block on a horizontal frictionless surface is
attached to a horizontal spring. The block is moving in
simple harmonic motion with amplitude A = 0.30 m and
period 
= 1.6 s.
a) What is the magnitude of the displacement x of the block when it
velocity has its largest magnitude?
Ans. _________________
b) What is the magnitude of the maximum velocity of the block?
Ans. _________________
c) What is the magnitude of the displacement x of the block when its
acceleration has its largest magnitude?
Ans. _________________
d) What is the magnitude of the maximum acceleration of the block?
Ans. _________________
e) How much time does it take the block to travel from x = 0.30 m to
x = -0.30 m?
Ans. _________________
(20 pts) 5. A large plastic sphere with mass 200 kg is held beneath the
surface of a lake by a rope attached to the bottom of the lake.
The density of the water is 1000 kg/m3. The tension in the
rope is observed to be 600 N. Calculate
a) the buoyant force exerted by the water on the sphere;
Ans. __________________
b) the volume of the sphere.
Ans. _________________
c) The rope is now cut, and the sphere rises to the surface of the lake. As it
floats at the surface, what fraction of its volume is submerged?
Ans. ________________