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PHY 108
Exam 1
Solution
The correct answer is in bold font.
1. Convert 100 mpg (100 mi/gal) to meters per cubic centimeter (m/cm3). 1 in = 2.54 cm, 1 mile = 1609 m, 1 mi = 5280
ft, 1 ft = 12 in, 1 gal = 3.8 l, 1 ml = 1 cm3.
a) 12.4 m/cm3
100
b) 27.6 m/cm3
c) 39.5 m/cm3
d) 42.3 m/cm3
mi #1609 m & #1 gal & # 1 l & # 1 ml &
m
"%
"%
"%
"%
= 42.3
(
(
(
3(
gal $ 1 mi ' $ 3.8 l ' $1000 ml ' $1 cm '
cm 3
2. Suppose there is a linear relationship between the height of water waves on a lake (the dependent variable, call it H,
measured in meters) and the speed of the wind (the independent variable, call it V, in m/s). The slope parameter of the
line fit to a graph of H vs. V will have units of
a) 1/s
c) s/m2
b) s
d) m2/s
Since the dependent variable is graphed on the vertical axis (thus H vs. V, like y vs. x), the units of the slope of the line fit
to that graph must be [units of H]/[units of V] = m/(m/s) = s.
3. The manufacturer of a 30 ft ladder warns that, when leaning the ladder against a vertical wall, the angle between the
ladder and the wall must not exceed 35˚. What is the maximum distance between the bottom of the ladder and the wall?
a) 8 ft
b) 11 ft
c) 14 ft
d) 17 ft
4. True or False: If you are adding at least three vectors, the sum of those vectors can never be zero.
False. Imagine adding three vectors that form the sides of an equilateral triangle. When you add them all tip to tail, you
get right back where you started, so the resultant is zero.
5. A water balloon is dropped from an unknown window in a tall building and hits the ground 3 s later. How high is the
window above the ground?
a) 31 m
b) 44 m
An object dropped from rest travels a distance d =
c) 59 m
d) 67 m
1 2 1
2
at = (9.8)( 3) = 44.1 m
2
2
6. A fighter jet goes from its cruising speed of 450 mi/hr to its attack speed of 700 mi/hr in a distance of 1 mile with
constant acceleration. The average speed of the jet during this acceleration is
a) 490 mi/hr
b) 520 mi/hr
!
c) 575 mi/hr
d) 650 mi/hr
At constant acceleration, the velocity increases linearly with time, so the average velocity is just the average value of the
height of the line on the v vs. t graph, which is just the numerical average of the endpoints. (450 + 700)/2 = 575.
7. You throw a ball upward from the base of Watterson Towers with an initial velocity of 20 m/s. On the way up, at what
time will it pass by a window 10 m above the ground?
a) 0.39 s
b) 0.58 s
c) 0.71 s
d) 0.96 s
2
Set x = 0 at the ground, positive upward, and you get 10 = 0 + 20t – 4.9t . Put that in the quadratic formula and you get t
= 0.58 s and 3.5 s. Choose the smaller one (the other one is when it passes that window on the way down).
8. A baseball is hit straight upward and is caught by the catcher when it returns to the ground. Which statement about the
ball’s flight after it leaves the bat is true? (Ignore the effects of air resistance.)
a)
b)
c)
d)
e)
The ball experiences upward acceleration on the way up and downward acceleration on the way down.
The ball experiences no acceleration on the way up and downward acceleration on the way down.
The ball experiences no acceleration during its flight.
The ball experiences downward acceleration during its flight.
The ball experiences greater acceleration when its velocity is greater.
9. You are standing just outside the airport boundary fence at the end of a runway, watching the planes land. They pass
directly over your head and land while flying in the direction you are looking (they land going away from you). A strong
wind is blowing from your left to right as you watch them land. How are the planes oriented in the air?
a)
b)
c)
d)
The nose of the plane points slightly to the left.
The nose of the plane points slightly to the right.
The nose of the plane points straight away from you.
The orientation of the plane’s nose cannot be determined from the information given.
Since the wind is coming from the pilot’s left, he must point the nose of the plane slightly to the left in order for the
plane’s velocity with respect to the ground to be parallel with the stripes on the runway, which are pointing directly away
from you (and the pilot). If you want to see this in action, search for crosswind landings at Kai Tak airport on YouTube.
10. If a plane can fly at 200 m/s (measured relative to the air) in still air, what will be its speed relative to the ground if it
flies directly into a 30 m/s headwind? The wind’s speed is measured relative to the ground.
a) 170 m/s
b) 200 m/s
c) 230 m/s
d) 260 m/s
In vector terms, v(plane with respect to ground) = v(plane with respect to air) + v(air with respect to ground). Since the
two vectors on the right are oriented opposite one another, you just subtract their magnitudes to get the magnitude of the
resultant velocity. Think of those nifty exercise pools that have a steady current equal to the speed with which you can
swim. If you swim against the current, your velocity with respect to the side of the pool is zero.
11. A ball rolls off a flat table, leaving the table with a horizontal speed of 6 ft/s. If the table is 3 ft tall, how far away
(horizontal distance) from the edge of the table does the ball land?
a) 1.4 ft
b) 2.6 ft
c) 3.3 ft
2
d) 4.8 ft
2
The vertical motion is freefall: h = (1/2)at or 3 = (1/2)(32.2)t , from which we get t = 0.433 s. The horizontal motion is
constant velocity: d = vt = (6)(0.433) = 2.6 ft.
12. Ignoring air resistance, which statement best describes the motion of a golf ball in flight?
a)
b)
c)
d)
The horizontal acceleration is dependent on the horizontal velocity.
The vertical acceleration is dependent on the vertical velocity.
Both the horizontal and the vertical motions are subject to acceleration.
The horizontal acceleration is zero.
13. A crate slides down an icy slope with constant speed. Which statement is true?
a)
b)
c)
d)
No forces act on the block, since its velocity is not changing.
The friction force must be zero, since the block is not slowing down.
The vector sum of all forces acting on the block points down the slope, in the direction of its motion.
The vector sum of all forces acting on the block is zero.
Since the crate has constant velocity (magnitude and direction), it experiences no acceleration, which requires that it feels
no net force.
14. You (weight = 130 lbs) stand on a bathroom scale (weight = 10 lbs). What is the force exerted by the scale’s platform
on you?
a) 10 lbs
b) 120 lbs
c) 130 lbs
d) 140 lbs
Consider a free body diagram of you. There are only two forces: your weight downward and the force from the scale’s
platform upward. Since the sum must be zero (you aren’t accelerating, since you’re standing still on the scale), the two
forces must be equal.
15. A block with an initial speed of 5 m/s slides along a rough floor (µk = 0.6) until it stops. How much time does this
motion take?
a) 0.85 s
b) 1.3 s
c) 2.4 s
d) 4.9 s
For a level problem, N = mg, so the kinetic friction force is µkmg in the opposite direction of the block’s motion. Put that
force into Newton’s 2nd Law, choosing positive to be in the direction of the block’s motion: – µkmg = ma to find that a =
–0.588 m/s2. Then v = v0 + at with v = 0, v0 = 5, and find t = 0.85 s.
16. A box weighing 500 N is suspended as shown below. If θ = 40˚, what is the horizontal pulling force P?
P
θ
500
a) 180 N
b) 250 N
c) 370 N
d) 420 N
Consider a free body diagram of the point where all the forces come together just above the box. You have a tension
force T up and to the left at a 40˚ angle from the vertical, P to the right, and 500 N down. For the y-direction, with
Fy = T cos(40) # 500 = 0 or T = 652.7 N. Then for the horizontal direction with positive to
positive upward, we have
"
the right, we have
"F
x
= P # T sin(40) = 0 , and we find P = 420 N.
17. Consider the earth’s orbit around the sun to be a circle with a radius of 93 million miles. If the earth orbits the sun
once every 365 !
days, what is the earth’s orbital speed? Recall that 1 mile = 1609 m.
!
a) 10,000 m/s
b) 20,000 m/s
c) 30,000 m/s
d) 40,000 m/s
6
dist 2"R 2" (93 #10 )(1609)
v=
=
=
= 29,813 m /s
time
T
365(24 )(60)(60)
18. You and some friends (total mass = 150 kg) swing on a 3 m rope over a lake. At the bottom of the swing, when the
speed is 4 m/s, what is the tension in the rope?
a) 1840 N
b) 1920 N
c) 2160 N
d) 2270 N
At the bottom of the swing, the tension T points upward and the total weight mg points downward. Choosing upward
(toward the center of the circular motion) as the positive direction, we have T – mg = mv2/r. Plug the numbers in and you
get T = 2270 N.
19. A coin sits on an old phonograph record, which spins at 33-1/3 revolutions per minute. What force(s) in the plane of
the record does the coin feel?
a)
b)
c)
d)
e)
An inward radial force and an equal, outward radial centrifugal force.
An outward centrifugal force only.
An inward radial force only.
An inward radial force and a tangential force in the direction of the coin’s motion.
The coin experiences no forces in the plane of the record.
20. If the radius of the cylinder in the carnival ride shown below is 4 m and the coefficient of friction µs = 0.7, what
minimum speed must the rider have to keep her from slipping down the wall of the cylinder?
The normal force from the wall of the cylinder points inward, toward the center. This gives rise
to a friction force µsN that must be equal to the rider’s weight mg. Thus µsN = mg or N = mg/µs.
Since N is the only radial force, N = mv2/r or mg/µs = mv2/r. The mass cancels, and v = 7.48 m/s.
a) 6.0 m/s
b) 7.5 m/s
c) 9.0 m/s
d) 10.5 m/s