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PRS_W08D1 Concept Questions Solutions
Concept Question: Compared to the amount of energy required to accelerate a car from
rest to 10 miles per hour, the amount of energy required to accelerate the same car from
10 mph to 20 mph is
1.
2.
3.
4.
the same
twice as much
three times as much
four times as much
Answer: 3. The energy increase in going from zero speed to speed v is (1 / 2)mv 2 . To go
from v to 2v is (1 / 2)m(2v)2 ! (1 / 2)mv 2 = (3 / 2)mv 2 .
Concept Question: Consider two carts, of masses m and 2m, at rest on an air track. If
you push first one cart for 3 s 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.
Answer: 1. The kinetic energy of an object can be written as
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: A particle starts from rest at x = 0 and moves to x = L under the
action of a variable force Fx (x) , shown in the figure. What is the particle's kinetic energy
at x = L / 2 and at x = L ?
1. Fmax L / 2 , and Fmax L
2. Fmax L / 4 , and 0
3. Fmax L , and 0
4. Fmax L / 4 , and Fmax L / 2
5. Fmax L / 2 , and Fmax L / 4
Answer 4: Since the particle starts from rest, the kinetic energy of the particle is equal tot
eh work done by the force. The work done by the force for a displacement !x = x f " xi is
xf
equal to the integral W ! " Fx dx = #K . The work is the area under the curve in the
xi
above diagram. So for the interval, x = 0 to x = L / 2 , the area is
W = !K = K(x = L / 2) = (1 / 2)Fmax (L / 2) = Fmax L / 4 .
For the interval form x = 0 to x = L , the area is just twice the previous case, so
W = !K = K(x = L) = Fmax L / 2 .
Concept Question: When a person walks, the force of friction between the floor and the
person's feet accelerates the person forward. The floor does
1. Positive work on the person.
2. Negative work on the person.
3. No work on the person.
Answer: 3. The friction is static and
! there is no displacement of the foot on the floor,
!
dr = 0 , when the force is applied F . So the contribution to the work
! !
dW ! F" dr = 0 . Keep in mind that a human being is not a rigid body. The correct
energy transformation is chemical energy is transformed into the motion of the
muscles which is transformed into kinetic energy of the center of mass.
Concept Question: A ball is given an initial horizontal velocity and allowed to fall under
the influence of gravity, as shown below.
The work done by the force of gravity on the ball is:
1. positive
2. zero
3. negative
Answer: 1. The force of gravity causes the ball to accelerate downward, so the
displacement has a component in the same direction as the force. Hence the work done is
positive. (The dot
of the ball's displacement and the downward force of gravity is
! product
!
positive, dW ! F" dr > 0 .)
Concept Question: A comet is speeding along a hyperbolic orbit toward the sun.
While the comet is moving away from the sun, the work done by the sun on the comet is:
1. positive
2. zero
3. negative
Answer: 3. The displacement of the comet has a component in the opposite direction as
the force on the comet so the work done is negative. (The comet's acceleration is always
toward! the sun; when the comet moves away from the sun, the work is negative,
!
dW ! F" dr < 0 ) .