Download EXAM 3 - University of Utah Physics

Dd
Physics 2210
Fall 2011
David Ailion
EXAM 3
PLEASE FILL IN THE INFORMATION BELOW:
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Discussion Instructor:
Marc Lindley
Jon Paul Lundquist Peter Peroncik
Rhett Zollinger
Useful Information:
1 ft = 12 in (exact)
1 mile = 5280 ft (exact)
1 day = 24 hr (exact)
gmoon = 1.67 m/s2 = 5.48 ft/s2
1 kg = 0.0685 slug
1 horsepower = 550 ft‫ڄ‬pounds/s (exact)
Rearth = 6.38 × 103 km
Rsun = 6.96 × 108 m
Rmoon = 1.74 × 103 km
k = 8.99 × 109 N‫ڄ‬m2/C2
eelectron charge = -1.60 × 10-19 C
1 m = 3.28 ft
1 hour = 3600 sec = 60 min (exact)
gearth = 9.80 m/s2 = 32.2 ft/s2
1 year = 365.25 days
1 N = 0.225 pound
Mearth = 5.98 × 1024 kg
Msun = 1.99 × 1030 kg
Mmoon = 7.35 × 1022 kg
G = 6.67 × 10-11 N‫ڄ‬m2/kg2
εo = 8.85 × 10-12 F/m
melectron = 9.11 × 10-31 kg
Dd
Physics 2210
Fall 2011
Name: ______________________________________
Unid: _______________________________________
Exam 3
Discussion TA: _______________________________
David Ailion
1
SHOW ALL WORK!!
Place a circle or box around each answer. Specify units for each answer.
Report all numbers to two significant figures.
Circle all that apply!
A.
[5 pts.] Which of the following are always true:
1.
2.
3.
4.
5.
B.
[5 pts.] Consider the work done by a spring on a mass attached to the end of the spring when the mass is
displaced from equilibrium by a distance Δx. Circle all correct answers.
1.
2.
3.
4.
C.
The work is always positive.
The work is always negative.
The spring force is conservative.
The spring force is non-conservative.
[5 pts.] As a simple pendulum swings back and forth, the forces acting on the suspended object are the
gravitational force, the tension in the supporting cords, and air resistance. Which of these forces do no work on
the pendulum.
1.
2.
3.
4.
D.
For an isolated mechanical system, the sum of the kinetic and potential energies is a constant.
If a conservative force does not depend on time (i.e., is a constant), the magnitude of the total work done
for a large displacement is simply the dot product of the force and the displacement.
If a conservative force does not depend on position, the magnitude of the total work done for a large
displacement is simply the dot product of the force and the force and displacement.
When power is involved, the forces must be non-conservative.
None of the above are always true.
Gravitational force.
Tension in the supporting cord.
Air resistance.
None of these.
[5 pts.] A generator generates energy that can be converted to work at a rate of P = At2 + Bt + C, where
A = 6.0 J/s3, B = -3.0 J/s2, and C = 12.0 J/s. Calculate the total energy generated between the third and sixth
seconds during the first six seconds of operation.


ate the angle between vector B and C in part C. Dd
Physics 2210
Fall 2011
Name: ______________________________________
Unid: _______________________________________
Exam 3
Discussion TA: _______________________________
David Ailion
2/3
SHOW ALL WORK!!
Place a circle or box around each answer. Specify units for each answer.
Report all numbers to two significant figures.
2.
[10 pts.] A 6.0 kg object, initially at rest in free space, “explodes” into three segments of equal mass. Two of the
segments are moving with equal speeds of 20 m/s with an angle of 60° between their directions of motion.
Calculate the total kinetic energy of the system immediately after the explosion.
3.
[10 pts.] Two particles of mass m and 3m are moving towards each other along the x-axis with the same initial
speed vi. Particle m is moving to the left and particle 3m is moving to the right. Each particle is coated with a
massless sticky cement, so that they stick together after the collision. Calculate the kinetic energy of the
composite particle after the collision. Compare it to the initial kinetic energy of the system and explain your
result.
Physics 2210
Fall 2011
Name: ______________________________________
Unid: _______________________________________
Exam 3
Discussion TA: _______________________________
David Ailion
4
SHOW ALL WORK!!
Place a circle or box around each answer. Specify units for each answer.
Report all numbers to two significant figures.
A baseball batter is observed to hit a ball of mass m = 0.15 kg that was pitched horizontally to him at a speed of 20 m/s.
The ball is observed to leave his bat with a speed of 30 m/s at an upwards angle of 30° with respect to the horizontal.
(a)
(b)
[10 pts.] Determine the angle that the impulse force exerted by the bat on the ball makes with the horizontal.
[10 pts.] If the mean impulsive force has a magnitude of 4500 N, calculate the approximate time that the bat was
in contact with the ball.
Physics 2210
Fall 2011
Name: ______________________________________
Unid: _______________________________________
Exam 3
Discussion TA: _______________________________
David Ailion
5
SHOW ALL WORK!!
Place a circle or box around each answer. Specify units for each answer.
Report all numbers to two significant figures.
A ball of mass m is connected by a strong string of length L to a pivot. A steady wind exerts a constant horizontal force

F on the ball as shown. Initially, the ball is held in place with the string vertical. The ball is then released and is
observed to swing up and down between it staring point and its maximum height H above its starting point.
(a)
(b)
(c)
[8 pts.] Derive an expression in terms of m, L, F, and g for the maximum height
H above the starting point before it swings down again.
[8 pts.] Now, if you raise it to a different height and then release it, it would not
move. This is called the equilibrium height Heq. Derive an expression for Heq in
terms of m, L, F, and g.
[4 pts.] If L = 80 cm, m = 300 gm, what is the value of Heq as F approaches
infinity?
Physics 2210
Fall 2011
Name: ______________________________________
Unid: _______________________________________
Exam 3
Discussion TA: ______________________________
David Ailion
6
SHOW ALL WORK!!
Place a circle or box around each answer. Specify units for each answer.
Report all numbers to two significant figures.
A massless spring is attached at one end to the lower end of a rough track.
The track sits at an angle θ with respect to the earth’s surface. A small mass
m is placed on the track and is pushed against the spring, but is not attached
to the spring. This results in a compression of the spring from its equilibrium
length by a distance d and the mass is held in this position. The mass is then
released and moves a distance x up the track before turning around and
returning to the spring. The coefficient of kinetic friction is µk and the spring
constant is k.
(a)
(b)
(c)
[8 pts.] Obtain an expression for the work done by friction when the mass m moves up the track a distance x
from its initial position to its final position where it turns around. This should be expressed in terms of the given
quantities: m, k, d, x, θ, µk, and g.
[8 pts.] Calculate the change in mechanical energy when the mass m moves up the track by the distance x.
Again, this answer should be expressed in terms of the given quantities: m, k, d, x, θ, µk, and g.
[4 pts.] Calculate the distance x, expressed in terms of m, k, d, θ, µk, and g.