7/4/13
Kinetic Energy and Work
Concept Questions with Answers
8.01
W06D1
Concept Question: Pushing Carts
Consider two carts, of masses m and 2m, at rest on an air
track. If you push one cart for 3 seconds and then the other
for the same length of time, exerting equal force on each,
the kinetic energy of the light cart is
1) larger than
2) equal to
3) smaller than
the kinetic energy of the heavy car.
Concept Q.: Pushing Against a Wall
The work done by the contact force
of the wall on the person as the
person moves away from the wall is
1.  positive.
8.01
W06D1
Today s Readings:
Chapter 13 The Concept of Energy and Conservation of
Energy,
Sections 13.1-13.8
Concept Question Ans. : Pushing
Carts
Answer 1. The kinetic energy of an object can be written as
K=
1 2 p2
mv =
2
2m
Because the impulse is the same for the two carts, the
change in momentum is the same. Both start from rest so
they both have the same final momentum. Since the mass
of the lighter cart is smaller than the mass of the heavier
cart, the kinetic energy of the light cart is larger than the
kinetic energy of the heavy cart.
Concept Question Answer: Pushing
Against a Wall
Answer 3. Because the person s
hand is at rest with respect to the
wall, the displacement of the point of
contact of the force is zero, hence
the contact force does zero work on
the person.
2.  negative.
3.  zero.
4.  impossible to determine from
information given in question and
the figure.
1
7/4/13
Concept Question: Work and Walking
When a person walks, the force of friction between the
floor and the person's feet accelerates the person
forward. The work done by the friction force is
1.  positive.
2.  negative.
3.  zero.
Concept Question: Work due to
Variable Force
A particle starts from rest at x = 0 and moves to x = L under
the action of a variable force F(x), which is shown in the
figure. What is the particle's kinetic energy at x = L/2 and at
x = L?
(1)  (Fmax)(L/2), (Fmax)(L)
Concept Question Answer:
Work and Walking
Answer 3. The point of contact between the foot and the
ground is at rest while the static friction force between the
ground and the foot is applied to the foot. So there is no
displacement of the point of contact hence the work done
by the friction force is zero.
Concept Question Answer:
Work Due to Variable Force
Answer: 4. The work is equal the area under the graph of
force vs. displacement. The work is also equal to the kinetic
energy. At x = L/2, the area is (1/2)(Fmax)(L/2) = (Fmax)(L/4) . At
x = L the area is 2(Fmax)(L/4) = (Fmax)(L/2) .
(2) (Fmax)(L/4), 0
(3) (Fmax)(L), 0
(4) (Fmax)(L/4), (Fmax)(L/2)
(5) (Fmax)(L/2), (Fmax)(L/4)
Concept Question
Two objects are pushed on a frictionless surface from a
starting line to a finish line with equal constant forces.
One object is four times as massive as the other. Both
objects are initially at rest. Which of the following
statements is true when the objects reach the finish
line?
1.  The kinetic energies of the two objects are
equal.
Concept Question Answer: Change in
Kinetic Energy
Answer 1. The force acting on both objects is the
same and the objects move the same distance,
therefore the work done on each object is the same.
Therefore each object has the same change in kinetic
energy. Because they both start form rest, their final
kinetic energies must be the same.
2.  Object of mass 4m has the greater kinetic
energy.
3.  Object of mass m has the greater kinetic energy.
4.  Not information is given to decide. 2