1. CH. 7 (50
POINTS) A
0.145 - kg ball is thrown upward with speed v1 = 16.0 m/s. At a certain
vertical height H, the ball has speed v2 = 2.00 m/s. As it rises
to height H, the
force of air friction does work of magnitude 4.00 J on the ball.
(a) (8) What is the direction of the air
friction force on the ball, up or down?
(b) (7) Is the work done by the air
friction force positive or negative? Explain briefly.
(c ) (10) Is
the work done by the gravitational force on the ball positive or negative?
Explain briefly.
(d ) (20)
What is the height H? For full
credit you must use either the work energy theorem or conservation of energy
in your solution.
(e) (5) Assume
the air friction force is constant. In parts (a) and (b), you addressed the direction
of the friction force. In this part, find the magnitude fk of the constant
force of air resistance exerted on the
ball during its upward motion.
2. CH. 7 (16 POINTS) A block of mass M = 1.000 kg has been
released from a position above a mass-less, un-deformed spring with platform. Study the
figure below. Just before the block
lands on the spring platform, its
speed is V1 . After the block lands on the platform, it
compresses the spring downward a distance h = 0.500 m before momentarily
coming to rest. The force constant of the spring is k = 60.00 N/m.
(a) (4) What is the kinetic energy of
the block just before landing on the spring platform? HINT: YOU MAY USE CONSERVATION OF ENERGY; TAKE INTO ACCOUNT THE GRAVITATIONAL AND SPRING POTENTIAL ENERGIES . YOU MAY DEFINE THE GRAVITATIONAL POTENTIAL ENERGY TO BE ZERO
AT THE INSTANT THE BLOCK FULLY COMPRESSES THE SPRING, I.E. AT THE BLOCK’S LOWEST VERTICAL LOCATION.
(b) (4) What is speed V1 of
the block just before landing on the spring platform?
(c) (4) What is the work done (in Joules) by
the spring during the compression? Is
the spring work positive or negative? Circle one. EXPLAIN BRIEFLY.
(d) (4 ) What is the
work done (in Joules) by the gravitational
force during the compression? Is
the gravitational work
positive or negative? Circle one. EXPLAIN BRIEFLY.
3.
CH. 8 (16 POINTS) On a
frictionless air track, a 0.5000
kg-glider moving to the right at 2.950
m/s collides with a 4.0000 kg glider at rest. The collision is elastic. Assume the right direction is
the positive direction of motion .
(a) (5 points) What is the velocity of the 0.5000 kg-glider after the collision? Indicate
the direction of motion after the collision, right or left. Is the velocity
positive or negative?
(b) (5 points)
What is the velocity of the 4.0000
kg-glider after the collision? Indicate the direction of motion after the
collision, right or left. Is the velocity positive or negative?
(c) (3 points) Using the velocities of parts (a) and
(b), compute the total kinetic energy of the system after the collision. Do
not round off during intermediate computations.
(d) (2 points) Using the initial velocity of 0.500-kg block before the
collision, compute
the kinetic energy before the
collision. Do not round off during
intermediate computations.
(e) (1 points) Are the answer to parts (c) and (d) equal? Should they be equal ? Explain.
4. CH. 8 ( 40
points) Two identical box cars of mass M are traveling in opposite directions
as shown below. Car A is traveling right with positive velocity + 24.0
m/s , and car B is traveling left with negative velocity – 32.0 m/s. The
velocities are shown below before the perfectly inelastic collision.
During the
collision, the cars lock together and the coupled cars move together with a
common velocity.
(a) (5) What direction do the coupled
cars move after the collision right or left?
Circle one.
(b) (20 ) What is the common velocity Vf
after the collision?
FOR THE NEXT PARTS ASSUME M = 1.000 kg.
(c) (5 points) Using the velocity of
part (b), compute the total kinetic energy of the system after the collision. Do
not round off during intermediate computations.
(d) (5 points) Using the initial velocities of the blocks before the
collision, compute
the kinetic energy before the
collision. Do not round off during
intermediate computations.
(e) (5 points) How much energy is lost to heat during the collision?
5. CH. 9 (12 points) An airplane propeller speeds up in its
rotation with uniform angular acceleration α = 1256.00 rad/s2. It is rotating counter clockwise and at t
= 0 has an angular speed of ωi
= 6280.00 rad/s.
(a) (4 points) How many seconds does it take the propeller to
reach an angular speed of 16,700.00 rad/s?
(b) (4 points) What is the angular speed (in rad/s) at t = 10.00 seconds?
(c) (4 points)
Through how many revolutions does the
propeller turn in the time interval between 0 and 10.00 seconds?
6. CH. 9 (12 points) A uniform solid sphere of radius R = 0.200
m and mass M = 1.80 kg starts from the
bottom of an inclined plane and rolls up the incline without
slipping. The initial translational speed of the center of
mass of the sphere
is vi cm = 8.40 m/s.
Show all work.
(a) (4 points) What is the initial
angular velocity ωi of the sphere
at the bottom?
(b) (4
points) What is the total kinetic
energy at the bottom?
(c) (4 points) What is the height vertical H
the sphere reaches when it momentarily comes to rest?
7. CH. 10 (35
POINTS) A solid, uniform
cylinder of mass M =
3600 kg and radius R = 4.0 m can rotate about an axis at the center. The
cylinder is subjected to the two steady
forces applied at the
opposite ends of a diameter shown. As you can see, the forces
are tangent to the cylinder rim.
(a) (5) Compute the moment of inertia I about the center.
(b) (10) What is the magnitude |
τ |of the net torque
about the center?
(c) (10) What is the cylinder’s
angular acceleration
α ?
(d) (10) Assume the cylinder starts it rotation from
rest when subjected to the two steady forces shown. What is the cylinder’s angular velocity
ω after a time period of 60.0 seconds?
8. CH. 10 (12
POINTS) A cylinder has R = 0.150 m and mass Mc = 5.00 kg. The cylinder turns without
friction about a stationary axle that passes through the center.
A light rope (of negligible mass) is wrapped around the cylinder and has a
4.00 kg uniform rectangular box suspended from its free left end. There is no slippage between rope and the cylinder surface.
(a) (5 points)
What is the magnitude τ of the torque on the cylinder about the center?
(b) (5 points)
What is the magnitude a of the downward linear acceleration of the box?
(c) (2
points) Assume the system starts its
motion from rest. What is the linear speed of the box after it has descended
a distance of
2.0 m?
|