PHY 131
Ch 6 to 9 Exam
The coefficient of kinetic
friction:
none of the above
external force is then applied
to the block to move it upward a
distance of 16 cm. While the
block is being raised by the
force, the work done by the
spring is
2g = k(0.06m)
k = 333 N/m
½ k .062 + ½ k .12
= .6
+ -1.66 = -1 J
1.
2.
A professor holds an eraser
against a vertical chalkboard by
pushing horizontally on it. She
pushes with a force that is
much greater than is required
to hold the eraser. The force of
friction exerted by the board
on the eraser increases if she:
pushes so her force is slightly
downward but has the same
magnitude
3.
4.
5.
A boy pulls a wooden box along a
rough horizontal floor at
constant speed by means of a
force P. Which of the following
must be true?
P = Ff and N = Fg
A 12-kg crate rests on a
horizontal surface and a boy
pulls on it with a force that is
30° below the horizontal. If the
µ = 0.40, the min magnitude of
force he needs to start the
crate moving is: Ff = μFN
FNet = mT a
Fcosθ - Ff = 0
Fcosθ =
Ff
Fcosθ = μ (mg + Fsinθ)
F = 72 N
When a certain rubber band is
stretched a distance x, it
exerts a restoring force F = ax
+ bx2, where a and b are
constants. The work done in
stretching this rubber band
from x = 0 to x = L is:
aL2/2 + bL3/3
6.
An object moving in a circle at
constant speed:
has an acceleration of constant
magnitude
7.
An ideal spring is hung vertically
from the ceiling. When a 2.0-kg
mass hangs at rest from it, the
spring is extended 6.0 cm from
its relaxed length. An upward
8.
9.
Name
speed of 3 m/s, collides with a
stationary 4-kg cart. The carts
stick together. The impulse
exerted by one cart on the
other has a magnitude of:
2(3) + 4(0) = (2+4)vf
vf = 1 m/s
Impulse = Δp =
2(3) – 2(1) = 4 Ns
13. When a particle suffers a headon elastic collision with another
particle, initially at rest, the
greatest fraction of kinetic
energy is transferred if:
A 1000-kg airplane moves in
straight flight at constant
speed. The force of air friction
is 1800 N. The net force on the
plane is:
FNet = mT a = 0
the incident and target particle have
the same mass
A force F = (4.1 N)i + (2.6 N)j –
(4.7 N)k acts on a mass of 2.3
kg as it moves in the x direction
at a speed of 7.2 m/s. What is
the rate at which the force is
doing work?
P = F v = 4.1 (7.2) =30 W
14. Two carts (A and B), having
spring bumpers, collide as
shown. Cart A has a mass of 2
kg and is initially moving to the
right. Cart B has a mass of 3 kg
and is initially stationary. When
the separation between the
carts is a minimum:
10. When a certain rubber band is
stretched a distance x, it
exerts a restoring force of
magnitude F = Ax, where A is a
constant. The work done by a
person in stretching this rubber
band from x = 0 to x = L is:
AL2/2
11. A hockey puck of mass m
traveling along the x axis at 4.5
m/s hits another identical
hockey puck at rest. If after
the collision the second puck
travels at a speed of 3.5 m/s at
an angle of 30° above the x
axis, is this an elastic collision?
4.5m = mv1f + m cos30(3.5)
vx1-f = 1.5 m/s
0 = m vy1-f + m sin30(3.5)
vy1-f = -1.75 m/s
v1-f2 = vx1-f2 + vy1-f2
v1-f = 2.3 m/s
KEo = ½m4.52 = m10.1 J
KEf = ½m2.32 + ½m3.52 = m8.8 J
KE is NOT conserved
12. A 2-kg cart, traveling on a
horizontal air track with a
the kinetic energy of the system is
at a minimum
15. A man sits in the back of a
canoe in still water. He then
moves to the front of the canoe
and sits there. Afterwards the
canoe:
is rearward of its original position
and not moving
16. A brick slides on a horizontal
surface. Which of the following
will increase the frictional
force on it?
Putting a second brick on top
17. A box with a weight of 50 N
rests on a horizontal surface. A
person pulls horizontally on it
with a force of 15 N and it does
not move. To start it moving, a
second person pulls vertically
upward on the box. If the
coefficient of static friction is
0.4, what is the smallest
vertical force for which the
box moves?
FNet
= mT a
15 – Ff = 0
15 - µ FN = 0
15 = .4 (50-Fup)
Fup = 12.5 N
18. A 400-N block is dragged along
a horizontal surface by an
applied force F. The coefficient
of friction is 0.4 and the block
moves at constant velocity. The
magnitude F is:
FNet
= mT a
Fx
– Ff = 0
Fx - µ F N = 0
Fx = .4 (400 - Fy)
.8F = .4 (400 - .6F)
F = 150 N
19. When a certain rubber band is
stretched a distance x, it
exerts a restoring force of
magnitude F = Ax, where A is a
constant. The work done by
stretching this rubber band
from x = 0 to L is: ½AL2
20. An 800-N passenger in a car
presses against the car door
with a 200 N force when the
car makes a left turn at 13 m/s.
The (faulty) door will pop open
under a force of 800 N. Of the
following, the least speed for
which the man is thrown out of
the car is:
Fc = mv2 / r
Fc = mv2 / r
2
¼mg = mv / r
800 = 80v2/67.6
r = 67.6 m
v = 26 m/s
21. Block A, (10 kg), rests on a 30°
incline. The coefficient of
friction is 0.20. Block B, (3.0
kg), is attached to the dangling
end of the string over a
frictionless pulley. The
acceleration of B is:
FNet
= mT a
(100sin30°-30) – Ff = (10+3) a
(20) - µ 100cos30° = 13a
a = 0.3 m/s2 up (0.2 m/s2 if g = 9.8 m/s2)
22. When a certain rubber band is
stretched a distance x, it
exerts a restoring force F = ax
+ bx2, where a and b are
constants. The work done in
stretching this rubber band
from x = 0 to x = L is:
aL2/2 + bL3/3
23. Three identical springs (X, Y, Z)
are arranged as shown.
When a 4.0-kg mass is
hung on X, the mass
descends 3.0 cm. When a
6.0-kg mass is hung on Y,
the mass descends:
F = kx
F = kx
40N = k 3cm
60 = 13.3 x
k = 13.3 N/cm
x = 4.5 cm
but each stretch
this much 9cm
24. In uniform circular motion,
acceleration and the velocity are
always perpendicular.
25. A man pushes an 80-N crate a
distance of 5.0 m upward along
a frictionless slope that makes
an angle of 30°with the
horizontal. His force is parallel
to the slope. If the speed of
the crate decreases at a rate
of 1.5 m/s2, then the work done
by the man is:
FNet
= mT a
Work = FΔx
F – sin30(80) = 8(-1.5)
= 28(5)
F = 28 N
= 140 J
26. If a projectile hits a stationary
target, and the projectile
continues to travel in the same
direction,
the mass of the projectile is greater
than the mass of the target
27. Blocks A and B are moving
toward each other along the x
axis. A has a mass of 2.0 kg and
a velocity of 50 m/s, while B
has a mass of 4.0 kg and a
velocity of –25 m/s. They
suffer an elastic collision and
move off along the x axis. The
kinetic energy transferred
from A to B during the collision
is:
mL vL + mR vR = po
2 (50) + 4 (-25) = po
po = pf = 0, so KE = 0 J
28. Blocks A and B are moving
toward each other. A has a
mass of 2.0 kg and a velocity of
50 m/s, while B has a mass of
4.0 kg and a velocity of –25
m/s. They suffer a completely
inelastic collision. The kinetic
energy lost during the collision
is:
KEf = 0 J (previous problem)
KEo = ½2(50)2 + ½4(-25)2
KEo = 3750 J All was lost
29. A projectile in flight explodes
into several fragments. The
total momentum of the
fragments immediately after
this explosion:
is the same as the momentum of the
projectile immediately before the
explosion
30. A light rope passes over a light
frictionless pulley attached to
the ceiling. An object with a
large mass is tied to one end
and an object with a smaller
mass is tied to the other end
and is then released from rest.
Which of the following
statements is true for the
system consisting of the two
objects?
None of the above statements are
true.
31. A 24-N horizontal force is
applied to a 40-N block initially
at rest on a rough horizontal
surface. If the coefficients of
friction are μs = 0.5 and μk =
0.4, the magnitude of the
frictional force on the block is:
FNet = mT a
24 – µ mg = mT a
24 – .5 40 = mT a
So it starts to move, must use μk
Ff = 0.4 (40N) = 16 N
32. The speed of a 4.0-N hockey
puck, sliding across a level ice
surface, decreases at the rate
of 0.61 m/s2. The coefficient of
kinetic friction between the
puck and ice is:
FNet = mT a
0 - Ff = mT a
0 – µ mg = .4(-.61)
µ = 0.061
33. A boy pulls a wooden box along a
rough horizontal floor at
constant speed by means of a
force P. Which of the following
must be true?
P > Ff and N < Fg
34. If a satellite moves above the
Earth's atmosphere in a
circular orbit with constant
speed, then:
its acceleration is toward the Earth
35. A ball is thrown upward into the
air with a speed that is greater
than terminal speed. It lands at
the place where it was thrown.
During its flight the force of
air resistance is the greatest:
just after it is thrown
36. Block A, (10 kg), rests on a 30°
incline. The coefficient of
friction is 0.20. Block B, (8.0
kg), is attached to the dangling
end of the string over a
frictionless pulley. The
acceleration of B is:
FNet
= mT a
(80-100sin30°) – Ff = (10+8) a
(30) - µ 100cos30° = 18a
a = 0.7 m/s2 down
37. An ideal spring is hung vertically
from the ceiling. When a 2.0-kg
mass hangs at rest from it, the
spring is extended 6.0 cm from
its relaxed length. A downward
external force is now applied to
the mass to extend the spring
an additional 10 cm. While the
spring is being extended by the
force, the work done by the
spring is:
F = kx
Work = ½kxo2 – ½kxf2
20N = k 6cm
= ½333(.062 –.162)
k = 3.3 N/cm
Work = -3.6 J
k = 333 N/m
38. A Boston Red Sox baseball
player catches a ball of mass m
that is moving toward him with
speed v. While bringing the ball
to rest, his hand moves back a
distance d. Assuming constant
deceleration, the horizontal
force exerted on the ball by his
hand is:
Ko – F f d = Kf
½ mv2 – F d = 0
F = mv2/(2d)
39. Two objects, X and Y, are held
at rest on a horizontal
frictionless surface and a
spring is compressed between
them. The mass of X is 2/5
times the mass of Y.
Immediately after the spring is
released, X has a kinetic energy
of 50 J and Y has a kinetic
energy of:
Momentum is linear relationship
KE has a squared relationship; 20 J
40. Block A, with a mass of 2.0 kg,
moves along the x axis with a
velocity of +5.0 m/s. It suffers
an elastic collision with block B,
initially at rest along the x axis.
If B is much more massive than
A, the velocity of A after the
collision is:
No work needed, essentially hitting
a massive wall, rebounds with same
speed. -5.0 m/s
41. Two identical carts travel at 1
m/s on a common surface. They
collide head-on and are
reported to rebound, each with
a speed of 2 m/s. Then:
if some other form of energy were
changed to kinetic during the
collision, the report could be true
42. A 3.0-kg cart and a 2.0-kg cart
approach each other on a
horizontal air track. They
collide and stick together.
After the collision their total
kinetic energy is 40 J. The
speed of their center of mass
is:
½(mL + mR)v2 = 40
½(2 + 3)v2 = 40
v = 4 m/s
43. A 2.0-kg block is attached to
one end of a spring with a
spring constant of 100 N/m and
a 4.0-kg block is attached to
the other end. The blocks are
placed on a horizontal
frictionless surface and set into
motion. At one instant the 2.0kg block is observed to be
traveling to the right with a
speed of 0.50 m/s and the 4.0kg block is observed to be
traveling to the left with a
speed of 0.30 m/s. We conclude
that:
mL vL + mR vR = 0
2(.5) + 4(-.3) ≠ 0
the motion was started with at least
one of masses moving
We have a pressurized launcher. A patented expanding foam is streamed into a vertical launch tube and propels an explosive
moldable “playdough type” ball. The expanding applies a force on the 10 kg ball of F = 20x4 (SI Units). If the ball explodes in 3
fragments at a height of 100 meters above the top of the tube, what was the length of the launch tube?
The 3 fragments are as follows:
fragment A, m = 3 kg, vx = 80 m/s, vy = 70 m/s, vz = 0;
fragment B, m = 2 kg, vx = 130 m/s, vy = -30 m/s, vz = 0; and
fragment C, m = 5 kg, vx = -100 m/s, vy = 60 m/s, vz = 0.
vx = Right (or East)  +, vy = Up  positive, vz = North (Into your page)  +
Explosion
y: pf = 3(70) + 2(-30) + 5(60) = pbefore
x: pf = 3(80) + 2(130) + 5(-100) = 0 kg m/s
2/2
Speed at launch tube exit
5/5
6/6
6/6
= 10(100) + ½ 452
K0 = ½ 10 63.42
K0 = 20,125 J
Alternate #16, Ch 7 to 9 principles as stated on the board
Work = ΔK
F dx
= 20125 J
20∫x4dx = 20125
4x5
= 20125
x = 5.5 m
vL = 1.24 m/s
5/5
3/3
= 10kg v@100m
13/13
po =
pf
0 = mL vL
A stationary block explodes into two pieces L and R that
+ mR vR
5/5
3/3
5/5
slide across a frictionless inclined ramp (by 30°) of
0
=
3(-1.24)
+
m
R 2.76
negligible distance and then into regions with friction,
m
=
1.35
kg
R
where they stop. Piece L, with a mass of 3.0 kg, encounters
a coefficient of friction μL = 0.80 and slides to a stop in
distance dL = 0.40 m. Piece R encounters a coefficient of
friction μR = 0.30 and slides to a stop in distance dR = 0.50
m. What was the mass of Piece R?
Right Block
Left Block
Ko
Ko
= Kf
mRg hR + ½ mRvR2 –
Ff
dR
mLg hL + ½ mLvL2 – Ff dL
= mLg hL + ½mLvL2
0 + ½mRvR2 - µ cos30 mR g .5
3(10) sin30(.4) + ½3 vL2 – Ff
dL = 0 + 0
0 + ½mRvR2 - 1.3 mR
2
5/5
5/5
6
+ 1.5 vL - µ cos30 3(10) .4 = 0
6/6
2/2
Work done by expanding foam
E0
=
Ef
m g h + ½ m v2 = m g hf + ½ m vf2
10(0) + ½v2
v0 = 63.4 m/s
2/2
450 kg m/s
v@100m = 45 m/s
2/2
2/2
2/2
This verifies no x-comp was transferred by external forces (wind, etc.)
5/5
=
=
=
=
Kf
mR g
hR + ½mRvR2
mR(10) sin30(.5) + 0
2.5 mR
(mR cancels)
6/6
vR = 2.76
OTHER VERSIONS
We have a pressurized launcher. A patented expanding foam is streamed into a vertical launch tube and propels an explosive
moldable “playdough type” ball. The expanding applies a force on the 10 kg ball of F = 12x2 (SI Units). If the ball explodes in 3
fragments at a height of 100 meters above the top of the tube, what was the length of the launch tube?
The 3 fragments are as follows:
fragment A, m = 5 kg, vx = 60 m/s, vy = 80 m/s, vz = 0;
fragment B, m = 3 kg, vx = -40 m/s, vy = 60 m/s, vz = 0; and
fragment C, m = 2 kg, vx = -90 m/s, vy = -70 m/s, vz = 0.
vx = Right (or East)  +, vy = Up  positive, vz = North (Into your page)  +
Explosion
x: pf = 5(60) + 3(-40) + 2(-90) = 0 kg m/s = pbefore_explosion
Speed at launch tube exit
E0
=
Ef
m g h + ½ m v2 = m g hf + ½ m vf2
y: pf = 5(80) + 3(60) + 2(-70) = 440 kg m/s = pbefore_explosion
pbefore_explosion = 440 kg m/s = m v@100m
v@100m = 44 m/s
Work done by foam
K0 = ½ 10 632
Work = ΔK
F dx
= 20,000 J
10(0) + ½v2
v0 = 63 m/s
= 10(100) + ½ 442
K0 = 20,000 J
12 x2 dx = 20000
4x3
= 20000
x = 17 m
We have a pressurized launcher. A patented expanding foam is streamed into a vertical launch tube and propels an explosive
moldable “playdough type” ball. The expanding applies a force on the 10 kg ball of F = 12x3 (SI Units). If the ball explodes in 3
fragments at a height of 100 meters above the top of the tube, what was the length of the launch tube?
The 3 fragments are as follows:
fragment A, m = 6 kg, vx = 40 m/s, vy = 70 m/s, vz = 0;
fragment B, m = 3 kg, vx = -40 m/s, vy = 50 m/s, vz = 0; and
fragment C, m = 1 kg, vx = -120 m/s, vy = -70 m/s, vz = 0.
vx = Right (or East)  +, vy = Up  positive, vz = North (Into your page)  +
Explosion
x: pf = 6(40) + 3(-40) + 1(-120) = 0 kg m/s = pbefore_explosion
Speed at launch tube exit
E0
=
Ef
m g h + ½ m v2 = m g hf + ½ m vf2
10(0) + ½v2 = 10(100) + ½ 502
v0 = 67 m/s
y: pf = 6(70) + 3(50) + 1(-70) = 500 kg m/s = pbefore_explosion
pbefore_explosion = 500 kg m/s = m v@100m
v@100m = 50 m/s
Work done by foam
K0 = ½ 10 672
K0 = 22,500 J
Work = ΔK
F dx
= 22500 J
12∫x3dx = 22500
3x4
= 22500
x = 9.3 m