Pickering, Tracey – Homework 10 – Due: Feb 13 2006, noon – Inst: Drummond
1
This
printout
should
have
10
questions.
Multiplechoice questions may continue on
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before answering.
The due time is Central
time.
001
(part 1 of 2) 10 points
A 25
.
3 kg mass attached to a spring scale rests
on a smooth, horizontal surface. The spring
scale, attached to the front end of a boxcar,
reads
T
= 33
.
4 N when the car is in motion.
m
If the spring scale reads zero when the car
is at rest, determine the acceleration of the
car, when it is in motion as indicated above.
Correct answer: 1
.
32016 m
/
s
2
.
Explanation:
Basic Concept:
Fictitious forces
Inertial/noninertial frames
Solution:
In the laboratory frame (which is an
inertial frame):
The block is accelerating with the car, with
an acceleration of
a
. This requires an external
force which must equal
m a
. Since the tension
T
is the
ONLY
available, external force we
know that
m a
=
T,
so that
a
=
T
m
=
33
.
4 N
25
.
3 kg
= 1
.
32016 m
/
s
2
Alternative derivation in the acceler
ated frame of the car:
The acceleration of the mass in the refer
ence frame of the car is
a
0
= 0; on the other
hand, the forces acting on the mass are the
tension
T
and the fictitious force
F
fic
=
ma
,
which acts in the direction opposite to the
car’s motion. Thus,
T

F
fic
=
T

ma
=
ma
0
= 0
and we get
a
=
T
m
= 1
.
32016 m
/
s
2
002
(part 2 of 2) 10 points
What would be the reading on the scale if the
boxcar were moving at a constant velocity?
1.
less than
T
, but greater than 0 N
2.
greater than
T
3.
0 N
correct
4.
T
5.
There is not enough information given to
tell which is correct.
Explanation:
The reading will now be zero. The easy way
to see this is to let the acceleration be zero,
and use this in the equation in part 1.
A more sophisticated way to see this is by
recognizing that the boxcar is now an inertial
frame since it is not accelerating. The block
is moving at the same velocity as the boxcar,
so the block is at rest in the boxcar’s frame
of reference.
The net force on the object at
rest in an inertial frame is zero. (Newton’s 1st
law)
003
(part 1 of 1) 10 points
A block of mass
m
accelerates with accelera
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 Fall '08
 Turner
 Force, Work, Sin, Cos, Pickering

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