Dot Product
Which of the following is the
best description
  of the dot
product A  B?

B
y


A
a) (length of A)  (component of B parallel to A)
b) (length of B)  (component of A parallel to B )
c) Ax Bx  Ay By
e) all of the above
d) AB cos 
x
Which of the following is the
best description
  of the dot
product A  B?
(a) 3 5 cos 26.6
(c) 6 xˆ  y
(e) (a) and (d)
B  2 xˆ  yˆ
y
26.60
A  3xˆ
(b) 6 xˆ  3 yˆ
(d) 6  0
x
Work
Suppose you want to ride your mountain bike up a steep
hill. Two paths lead from the base to the top, one twice as
long as the other. Compared to the average force you would
exert if you took the short path, the average force you exert
along the longer path is
(a) four times as small.
(b) three times as small.
(c) half as small.
(d) the same.
(e) undetermined—it depends on the time taken.
A
The platform on the right pushes the
blocks up at a constant velocity
B
C
v
1. Does the block A do work on block B ?
a) yes
b) no
2. Is the work done by block A on block B
a) negative
b) positive
c) zero
3. Is the work done by block B on block A
a) negative
b) positive
c) zero
4. Is the work done by the earth on block C
a) negative
b) positive
c) zero
5. Is the net work done on the block C
a) negative
b) positive
c) zero
Gravitational Potential Energy
In the expressions below, h is a height and m is a mass
Recall:
(1) Energy is measured in joules
1 J = 1 N m = 1 kg m2s-2
(2) W= F·s = m·a·s
Which of the expressions below is the gravitational potential energy
of a body?
(a) mg
(b) mh
(d) mgh
(e) ½mh2
(c) gh
Use dimensional analysis and any other arguments to
prove to a colleague that your answers are correct.
h
m
If we choose the gravitational potential energy to be zero
for an object sitting on the table, what is its potential
energy when on the floor?
a) positive
b) negative
c) zero
Thermal Energy Due to Kinetic Friction
In the expressions below, )x is a change in length, N is a normal
force between two surfaces in contact, m is a mass, µk is a
coefficient of kinetic friction
Recall: 1 J = 1 N m = 1 kg m2s-2 and W= F·s = m·a·s
Which of the expressions below is the thermal energy due to kinetic
friction?
(a) µkN
(b) µkg)x
(d) N)x
(e) ½µkmg)x 2
(c) µkN)x
Use dimensional analysis and any other arguments to
prove to a colleague that your answers are correct.
Kinetic Energy
In the expressions below, v is a speed, )v is a change in speed and m
is a mass
Recall:
Energy is measured in joules: 1 J = 1 N m = 1 kg m2s-2
Which of the expressions below is the kinetic energy of a moving
body?
(a) mv
(b) m)v
(c) ½mv2
(d) ½m()v)2
Use dimensional analysis and any other arguments to
prove to a colleague that your answers are correct.
Two marbles, one twice as heavy as the other, are dropped to the
ground from the roof of a building. Just before hitting the
ground, the heavier marble has
(a) as much kinetic energy as the lighter one.
(b) twice as much kinetic energy as the lighter one.
(c) half as much kinetic energy as the lighter one.
(d) four times as much kinetic energy as the lighter one.
(e) impossible to determine
Potential Energy of a Spring
In the expressions below, x is a position, )x is a change in length
and k is a spring constant in N/m.
Recall:
Energy is measured in joules: 1 J = 1 N m = 1 kg m2s-2
Which of the expressions below is the potential energy of a spring?
(a) kx
(b) k)x
(d) ½kx2
(e) ½k)x2
(c) -k)x
Use dimensional analysis and any other arguments to
prove to a colleague that your answers are correct.
Work & Energy
A spring-loaded toy dart gun is used to shoot a dart straight up in the
air, and the dart reaches a maximum height of 24 m. The same dart is
shot straight up a second time from the same gun, but this time the
spring is compressed only half as far before firing. How far up does
the dart go this time, neglecting friction and assuming an ideal
spring?
(a) 96 m
(b) 48 m
(c) 24 m
(d) 12 m
(e) 6 m
A cart on an air track is moving at 0.5 m/s when the air is
suddenly turned off. The cart comes to rest after traveling 1 m.
The experiment is repeated, but now the cart is moving at 1 m/s
when the air is turned off. How far does the cart travel before
coming to rest?
(a) 1 m
(b) 2 m
(c) 3 m
(d) 4 m
(e) impossible to determine
A block initially at rest is allowed to slide down a frictionless ramp
and attains a speed v at the bottom. To achieve a speed 2v at the
bottom, how many times as high must a new ramp be?
(a) 1
(b) 2
(c) 3
(d) 4
(e) 6
Suppose you drop a 1-kg rock from a height of 5 m above the
ground. When it hits, how much force does the rock exert on the
ground?
(a) 0.2 N
(b) 5 N
(c) 49 N
(d) 9.8 N
(e) impossible to determine
The block is accelerating as it moves
down the plane. Which of the
following statements is (are) correct?
v=0 m/s
a
v
h
(a) The thermal energy produced in the sliding surfaces equals the
work done by gravity (the gravitational force of the earth on the block).
(b) The total work done by gravity on the block equals the total amount
of kinetic and thermal energy at the bottom.
(c) The kinetic energy of the block at the end is
equal to the potential energy of the block at the
start.
(d) The total work done by gravity equals the
decrease in the block’s potential energy.
(e) Answers (b) and (d)
If the block is accelerating and
)K is the change in the
block’s kinetic energy, the
work done by the constant
applied force is
(a) Fs
(b) Fs + )K
(c) F cos2 s
 
(d) F  s + )K
(e) (b) and (d)
F
2
s
If the block is accelerating and )K
is the change in the block’s kinetic
energy, the work done by
 the
constant applied force F is
F
2
s
(a) F cos2 s + )K + thermal energy in the rubbing surfaces
(b) )K + thermal energy in the rubbing surfaces
(c) Fs + )K
(d) F cos2 s
(e) Fs

The block below is pulled to the right by the force F at a
constant velocity

F

fk
k
mg

s
N
coefficient
of friction
What is the work
 done by the ‘puller’ to move it through
displacement s
a) Fs
b)  f k s
c) F cos  s
d) F sin  s
e)  F cos   f k  s

The block below is pulled to the right by the force F at a
constant velocity

F

fk
k
mg

s
N
coefficient
of friction
What is the work
 done by friction as the block is pulled a
displacement s ?
a) f k s
b)  f k s
c) F cos  s
d) F cos  s  f k s
e) F cos  s  f k s
A box is pulled up a hill a distance s
by a rope under tension T. The FBD
of the box is shown on the right
s
T
T
2
fk
1. The work done by the rope is
(a) T s
(b) (T - fk) s
(c) (T - fk - mg sin2) s (d) zero
2. The work done by the friction is
(a) fk s
(b) -fk s
(c) fk cos2 s
3. The work done by the normal force is
(a) Nsin2 s
(b) Ncos2 s
(c) -Nsin2 s
(d) -Ncos2 s (e) zero
4. The work done by gravity is
(a) mg sin2 s (b) -mg sin2 s (c) mg cos2 s
(d) -mg cos2 s (e) zero
(d) zero
mg N
Work and F(x) Graphs
Sketch the graph of the force F required to stretch the spring a
distance x.
Which of the following is most correct?
F
F
x
x
(a)
(b)
F
F
x
(c)
x
(d)
A spring has a force constant k = 8 N/m. Therefore, the plot of force
vs. extension of the spring looks like
F
slope = 8 N/m
x
0.2 m
What is the work required to extend the spring a
distance of 0.2 m?
(a) (1.6 N)(0.2 m)
(b) ½(1.6 N)(0.2 m)
(c) (8 N/m) (0.2m)
(d) None of the above.
A boy pulls a cart across flat ground with a force parallel to the
ground which varies with distance as sketched below
How much work has the boy done in this time?
F
F
20 N
x(m)
10
20 25
a) zero
b) 250 N
c) 350 N m
d) 500 J
e) Can’t tell because the time is not given
Potential-Energy Diagrams
The figure below is a potential-energy diagram U(x) of a ball on a
frictionless track.
U
Starts from rest
D
A
B
C
Which of points A B C D is (are)…
(a) …the point of maximum velocity
(b) …a point of zero velocity
(c) …a point of unstable equilibrium
(d) …a point of stable equilibrium
x
The figure on the right
following is potential-energy
diagram for a mass vibrating
horizontally on the end of a
spring.
Massed
released
U
U=1/2 kx2
x
0
Neglecting friction, which of the following diagrams best represents
the kinetic energy of the mass?
(A)
(B)
K
0
x (C)
K
K
0
0
x
x
Power
A sports car accelerates from zero to 30 mph in 1.5 s. How long
does it take for it to accelerate from zero to 60 mph, assuming the
power of the engine to be independent of velocity and neglecting
friction?
(a) 1.5 s
(b) 3 s
(c) 4.5 s
(d) 6 s
(e) 9 s
A person pulls a box along the
ground at a constant speed. If we
consider Earth and the box as our
system, what can we say about the
net external force on the system?
(a) It is zero because the system is isolated.
(b) It is nonzero because the system is not isolated.
(c) It is zero even though the system is not isolated.
(d) It is nonzero even though the system is isolated.
(e) none of the above