Physics 201 MWF10:20 Fall 1998 (Ford)
Exam III Chapts. 8--11 in Cutnell and Johnson, 4th ed.
(18 pts) 1. A block with mass 3 kg is attached to a horizontal spring and moves on a
horizontal, frictionless surface. The block undergoes simple harmonic motion wih a
period of T = 0.4 s and amplitude A = 0.2 m.
a) What is the maximum kinetic energy of the block during its motion?
Ans. _______________
b) What is the maximum potential energy stored in the spring during the motion?
Ans. _______________
c) What is the maximum acceleration of the block during its motion?
Ans. ________________
(20 pts) 2. A large horizontal platform rotates without friction about an axle
through its center. The platform has moment of inertia I = 80 kg·m2
and is initially rotating with an angular velocity of 4.0 rad/s.
A bag of gold coins with mass 40 kg is then dropped vertically onto the
platform, at a distance of 2.0 m from the axle. Assume that the bag of
coins can be treated as a point mass. After the bag has come to rest relative
to the platform, what is
a) the final angular velocity of the platform;
Ans. _______________
b) the final kinetic energy of the system (platfrom plus bag)?
Ans._________________
(22 pts) 3. A rope of negligible mass is wrapped around a pulley that turns without
friction about an axis through its center. A 15-kg block is suspended from the
free end of the rope. The radius of the pulley is R = 0.20 m. The system is released
from rest, and the downward acceleration of the block is observed to be 3 m/s2.
a) What is the tension in the rope, while the block is moving?
Ans._______________
b) What is the angular velocity of the pulley 2.0 s after the system is released?
Ans._______________
c) What is the moment of inertia of the pulley, for an axis through its center?
Ans.________________
(20 pts) 4. A uniform board with mass 6.0 kg is attached to the floor by a
hinge that rotates freely, without friction. The board is held at an angle
of 36.9° to the wall by a spring attached to the end of the board. The
spring is at right angles to the board and has force constant 200 N/m. Find the
amount the spring is stretched from its unstretched length.
Ans._________________
(20 pts) 5. A small block has mass 0.50 kg. The block is suspended from a string.
When the block is completely immersed in water the tension in the string is 3.5 N.
When the blcok is completely immersed in oil the tension in the string is 3.8 N. The
density of water is 1000 kg/m3.
a) What is the volume of the block?
Ans._________________
b) What is the density of the oil?
Ans._________________