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First Semester Final
Exam Prep
Name:
Date:
A horizontal beam of weight W is supported by a hinge and cable as shown below.
C able
P
W
1. The force exerted on the beam by the hinge at point P has a vertical component which must be...
A. nonzero and point up
c. nonzero, but quantitative information is necessary to
determine its direction
b. nonzero and point down d. equal to zero
e. equal in magnitude to the weight
of the beam
I.
An airplane is flying with a velocity of 240m/s at an angle of 30.0° with respect to the horizontal, as the
drawing shows. When the altitude of the plane is 2.4 km, a flare is released from the plane. The flare hits
the target on the ground.
A. What is the horizontal component of the initial velocity? cos d 240 m/s
B. What is the vertical component of the initial velocity? sin d 240 m/s
C. How long (time) does it take the flare to reach the ground? K 0 + U0 = K (use vertical velocities)
D. What is the horizontal displacement between the release point and the target? x=vt (use horizontal v)
II. An amusement park ride consists of a large vertical cylinder that spins about its axis fast enough that any
person inside is held up against the wall when the floor drops away. The coefficient of static friction
between the person and the wall is µ, the radius of the cylinder is r , and acceleration due to gravity is g.
A. Prepare a free body diagram for the rider.
f
N
mg
°
B. Determine ( in terms of r, g, and µ ) the minimum speed of the rotating cylinder to keep the rider on the
wall. f= (mu) N f=mg N=Fc=m(v2/r) mg=(mu)N N=mg/mu
mg/mu= m(v2/r)
then solve for v
C. If µ = 0.5 and the diameter of the rotating cylinder is 5m, what would be the minimum number of
rotations made by a rider in one minute? Use numbers and plug into above equation
The data shown in the graph below was obtained from an ideal spring stretched vertically by a hanging
weight.
3. What is the value of the spring constant?
a. 10N/m
b. 50N/m
c. 0.1N/m
d. 5N/m
4. What is the work done stretching the spring to a length of 0.3m?
A. 0.45J
c. 1.25J
mass
b. 0.90J
d. 10J
E. 10m/N
e. Impossible without
The same spring is attached to a fixed post on one end, and a movable mass (0.200kg) on the other as the
diagram below illustrates. The mass is displaced 0.3m to the left, and is then released. Assume that no
dissipative forces act within the system.
5. What will be the velocity of the mass as it passes through the equilibrium length of the spring?
a. 4.15m/s
C. 2.12 m/s
e. 0.09m/s
b. 3.53m/s
d. 1.50m/s
6. How much work will the mass do compressing the spring beyond the equilibrium position?
A. 0.45J
c. 1.25J
e. 0.09J
b. 0.90J
d. 10J
7. Suppose the system shown above was not frictionless, and that after oscillating for one minute the mass
came to rest at its equilibrium position. What would be the rate of energy dissipation for the system?
a. 75 watts
c. 100 watts
e. 0.02 watts
B. 7.5x10-3 watts
d. 27 watts
III.
.
A 0.30 kg object moves along a straight line. The net force acting on the object varies with the object's
displacement as shown in the graph above. The object starts from rest at displacement x = 0 and time t= 0
and is displaced a distance of 20m. Determine each of the following.
A. The acceleration of the particle when its displacement x is 8m. a=F/m
B. The time taken for the object to be displaced the first 12m. x=1/2at 2
C. The amount of work done by the net force in displacing the object the first 12m. W=Fd (from graph)
D. The speed of the object at displacement x =12m. W=K solve for v
E. The final speed of the object at displacement x=20m. area under graph is work=K; solve for v
A block oscillates without friction on the end of a spring as shown above. The minimum and maximum
lengths of the spring as it oscillates are, respectively, x min and xmax. The graphs below represent
quantities associated with the oscillation as functions of the length x of the spring.
a.
b.
c.
d.
E.
8. Which graph can represent the total mechanical energy of the block spring system as a function of x?
a. a
b. b
c. c
d. d
e. E
9. Which graph can represent the kinetic energy of the block as a function of x?
a. a
b. b
c. c
d. D
e. e
10. The figure above shows a rough semicircular track whose ends are at a vertical height h. A block placed
at point P at one end of the track is released from rest and slides past the bottom of the track. Which of the
following is true of the height to which the block rises on the other side of the track?
a. It is equal to h/2π
c. h/2 E. It is between zero and h; the exact height depends on how much
energy is lost to friction.
b. h/4
d. h
IV.
As shown above, a 0.20 kg mass is sliding on a horizontal, frictionless air track with a speed of 3.0 meters
per second when it instantaneously hits and sticks to a 1.3 kg mass initially at rest on the track. The 1.3 kg
mass is connected to one end of a massless spring, which has a spring constant of 100 newtons per meter.
The other end of the spring is fixed.
A. Determine the linear momentum of the 0.20 kg mass immediately before the impact. P=mv
B. Determine the kinetic energy of the 0.20kg mass immediately before the impact. K=1/2mv 2
C. Determine the linear momentum of the combined masses immediately after impact. Same as A.
D. Determine the kinetic energy of the combined masses immediately after impact. Use momentum to
figure v after collision. Use this v to calculate the kinetic energy.
E. Determine the maximum compression of the spring after the impact. K=Ue soleve for x
11. This event illustrates what basic principle?
a. conservation of energy
faster when spun
B. conservation of linear momentum
c. projectile motion
e. clothes dry
d. L=L’
12. To weigh a fish, a person hangs a tackle box of mass 3.5 kg and a cooler of mass 5 kg from the ends of
a uniform rigid pole that is suspended by a rope attached to its center. The system balances when the fish
hangs at a point 1/4 of the rod's length from the tackle box. What is the mass of the fish?
a. 1.5 kg
b. 2kg
C. 3kg
d. 6kg
e. 6.5kg
V.The spring shown above oscillates with simple harmonic motion at a frequency of 0.796 Hz when a
mass m of 2kg is attached to it.
A. What is the period of the oscillation? T=1/frequency
B. What is the spring constant of the spring? T=2pi sqrt m/k
solve for k
The mass m (2kg) shown above is brought to rest. A second block with mass 2m (4kg) moving with a
velocity of 2m/s collides inelastically with the stationary mass. The system enters into simple
harmonic motion after the collision.
A. What is the momentum of the combined blocks after the collision?
before the collision
Same as momentum of 2m block
B. What is the velocity of the connected masses after the collision? Use p/ 3m
C. What is the maximum Ue of the spring after the collision? U e=K
D. What is the amplitude A of the simple harmonic motion after the collision? Solve U e for x
E. What is the frequency of the oscillation of the connected masses? Use T=2pi sqrt m/k
F. What is the velocity of the connected masses at x=-0..20m?
Figure 1.2
M
m
13. The system in figure 1.2 has mass M on a frictionless table and a cord running over a massless, frictionless pulley
to mass m. If g is the acceleration due to gravity, the acceleration of the system should be... a=mg/(M+m)
14. A projectile is launched from ground level with an initial velocity Vo at an angle.  has a value >0° and <90°.
Which of the following graph sets correctly describes the motion of the object.
a.
b.
c.
d.
E.
Figure 1.6
15. The total displacement for the object described by figure 1.6 after 13 seconds is...
A. 60m
c. 88m
b. 44m
d. 52m
16. Which of the following pairs accurately describes p vs t and a vs t graphs derived from figure 1.6?
p
p
p
t
t
a
o
t
a
o
t
p
t
a
A.
p
a
o
t
b.
o
t
c.
d.
t
o
t
a
e.
t
e.
A
6 kg
B
C
D
E
8 kg
17. Two objects, of masses 6 and 8 kilograms, are hung from ends of a stick that is 70 cm long and has marks every
10cm as shown above. If the mass of the stick is negligible, at which of the points indicated should a cord be attached if
the stick is to remain horizontal when suspended from the cord?
a. A
b. B
c. C
D. D
e. E