Download PHYS 201 General Physics

PHYS 201 General Physics
Final Exam Review Sheet
• The final exam will be comprehensive. Look over your midterm exam review sheet and
the midterm exam.
• Here are some problems of the type you may expect on the exam. Many of these have
been used in previous examinations.
1. A 150-gram arrow is shot straight up with a speed of 30.0 m/s. It reaches a height of
40.0 m. How much energy is lost due to air friction on the way up? (8.7 J)
2. What is the average force needed to stop a bullet of mass 20.0 grams and speed 500
m/s as it penetrates a wooden block to a distance of 12.0 cm? (2.08×104 N) Assuming
a constant force, how long does it take to stop the bullet? (0.48 ms)
3. Suppose a child on a sled has just reached the bottom of 8th-street hill after sliding
down the snow–covered slope. The mass of sled plus child is 20 kg, and the coefficient
of friction between sled and snow is 0.08. The sled is travelling 10.0 m/s when it reaches
the level street at the bottom of the hill. (A) Draw a free-body diagram showing all
forces on the sled & child. (Consider them a single object.) (B) Calculate the force of
friction on the sled.
(C) Calculate the acceleration of the sled. (-0.78 m/s2 )
(D) How far will the sled travel after reaching the bottom of the hill? (64 m)
4. Now consider a 25-kg sled travelling down a snow–covered slope which makes an angle
of 15◦ with the horizontal. (A) Draw a free-body diagram of the sled. (B) Calculate
the component of weight which is parallel to the slope of the hill. (C) Calculate the
“normal force” of the hill on the sled. (D) The coefficient of kinetic friction between sled
and snow is 0.3. Is the sled speeding up or slowing down? Calculate the acceleration
(positive or negative) of the sled.
(B): 63 N
(C): 236 N
(D): slowing, -0.32 m/s2
5. Fred Fearless is the “human cannonball” of a travelling circus. He is shot from a
specially-made cannon which gives him a velocity of 15 m/s leaving the cannon muz˙
What is the vertical
zle. The angle the cannon makes with the horizontal is 35◦ (A)
component of Fred’s velocity upon leaving the cannon muzzle? (B) What is the horizontal component of velocity? (C) How long does it take him to reach his maximum
height after leaving the cannon? (D) How far from the cannon should the net to catch
Fred be placed? Assume that it is at the same height above ground as the muzzle
of the cannon. (E) Find Fred’s velocity (magnitude and direction) 1.00 seconds after
he leaves the cannon. (C): 0.88 s ; (D): 21.6 m; (E): 12.3 m/s at 5.5◦ below the
horizontal.
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6. A boccè ball is dropped on the planet Uranus. It drops 15 cubits in 2.0 seconds.
Assuming that it continues falling freely, how many cubits does it drop in the next 4.0
seconds? (120 cubits)
7. We show here a graph of velocity versus time for a rubber ball dropped on a concrete
floor.
(a) What was the ball’s average velocity from time t = 4 to t = 7 seconds? From t
= 0 to t = 4 seconds?
(b) How far did the ball travel from time t = 2.0 s to t = 4.0 s? (–3.0 m)
(c) Was this ball dropped on the earth? (no)
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Velocity, m/s
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1
0
1
2
3
4
5
6
7
8
9
-1
-2
-3
-4
TIME, S
8. An Atwood’s machine is set up, with a 2.0 kg mass hanging on one side of a pulley and
another, unknown mass on the other side. When the masses are let go, the acceleration
of the 2.0 kg mass is found to be 2.0 m/s2 downward. (A) What is the tension in the
string? (B) What is the unknown mass?
9. Suppose you are a passenger in a car and the driver has an object hung from his rearview mirror. The reason the driver did that is that, being highly educated (i.e. having
taken physics) he knows that he can use this object as an accelerometer. While the
driver is accelerating the car through a measured quarter–mile, you measure the angle
at which the object is hanging and find it to be 25◦ from the vertical. (A) Draw a
free-body diagram of the hanging mass in the above situation. (B) The mass of the
object is 100 g. What is the tension in the string? Hint: the net vertical force must be
zero. (1.08 N) (C) What is the horizontal component of the tension in the string?
(0.46 N) (D) What is the acceleration of the car? (4.6 m/s2 )
10. Draw representative position-vs-time graphs for (A) an object moving at a constant
positive velocity; (B) an object moving at a constant negative velocity; (C) an object
undergoing a positive acceleration; and (D) an object undergoing a negative acceleration.
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11. A 2500-kg car is traveling 60 km/hr on a level highway. It is a rainy day and the
coefficient of kinetic friction between the tires and the road is 0.15. The driver panics
and hits the brakes, locking up all four wheels. Calculate the work done by friction as
the car slides 50 m.
12. Suppose a child drops a flower pot weighing 20 N from a window which is 3.0 m above
a sidewalk.
(a) Before the child drops it, what is the gravitational potential energy of the flower
pot, relative to the sidewalk? [60 J ]
(b) What is the kinetic energy of the flower pot just before it hits the sidewalk?
[emph60 J]
(c) What is the kinetic energy of the flower pot when it is halfway between the window
and the sidewalk? [30 J ]
(d) What is the velocity of the flower pot when it is halfway between the window and
the sidewalk? [5.4 m/s]
(e) At what point is the velocity of the flower pot half of its final velocity (v: just
before it hits the sidewalk)?
13. A bicycle rider is coasting along, on level ground, with an intial speed of 8.0 m/s. The
combined mass of rider and bicycle is 100 kg. Because of friction, the bike gradually
slows and comes to rest in a distance of 80.0 m.
(a) What is the initial kinetic energy of rider and bike?
(b) Using the work-energy theorem, calculate the total kinetic energy when the bike
has gone a distance of 40 m. [1600 J ]
(c) Calculate the speed of the bike when it has gone a distance of 40 m.
(d) Suppose the bike and rider start out coasting at a speed of 4.0 m/s instead of 8.0
m/s. How far will the bike go before stopping in this case? [20 m]
(e) Calculate the force of friction on the bike. (Use the work-energy principle).
(f) Suppose the rider starts pedalling to keep the speed of the bike at a constant 8.0
m/s. What is the power the rider must supply to keep the bike moving at this
speed? [320 W ]
14. A man on a bicycle is moving at 20 m/s on the level. He approaches a hill and coasts
up the hill. As he goes over the top, he is moving at 5.0 m/s. How high is the hill?
Ignore friction.
15. A guitar string of length 35 inches vibrates in its fundemental mode at a frequency of
220 Hz. What is the speed of the waves traveling along the string? (1280 ft/s or 0.39
km/s)
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16. A mountain climber is testing a new rope. He ties one end to a high tree limb and the
other end to himself. The length of the rope is 15 m and the mass of the man is 80 kg.
He finds that the rope stretches a distance of 5.0 cm when supporting all of his weight.
(a) What is the “spring constant” of the rope? (b) When the man is hanging from the
rope, he may oscillate up and down. What is the frequency of this oscillation? (2.23
Hz)
17. A simple pendulum has a period of 2.00 seconds on the Earth. (a) What is the
length of this pendulum? (99.3 cm) (b) If the amplitude of the swing is 5.00◦ , what
is the maximum speed of the pendulum bob? Determine this in two different ways.
(0.272 m/s) (c) What is the maximum acceleration of the pendulum bob, and at what
positions does this occur? Find this value in two different ways. (0.85 m/s2 ) (d) What
would the angular frequency and the period of this pendulum be on the moon, where
the acceleration of gravity is 0.165 that of Earth?
18. A simple pendulum that has a period of exactly 2.000 seconds at the Greenwich Observatory in England, where g = 9.812 m/s2 , is taken to Paris, where it loses 20 seconds
a day. What is the acceleration due to gravity in Paris? (9.807 m/s2
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