HomeWork 8 solutions
Physics 203
1.
Chapter 6 problem 26
REASONING
a.
The magnitude
s
of the displacement that occurs while the snowmobile coasts to a halt is the distance
that we seek.
The work
W
done by the net external force
F
acting on the snowmobile during the coasting phase
is given by
W
= (
F
cos
θ
)
s
(Equation 6.1), and we can use this expression to obtain
s
.
To do so, we will need to
evaluate
W
.
This we will do with the aid of the workenergy theorem as given by
22
11
f0
W
mv
mv
=
−
(Equation
6.3), since we know the mass
m
and the final and initial velocities
v
f
and
v
0
, respectively.
The net external force
F
during the coasting phase is just the horizontal force of kinetic friction (magnitude =
f
k
), since the drive force
is shut off and the vertical forces balance (there is no vertical acceleration).
This frictional force has a
magnitude of 205 N.
This follows because, while the snowmobile is moving at a constant 5.50 m/s, it is not
accelerating, and the drive force must be balancing the frictional force, which exists both before and after the
drive force is shut off.
Finally, to use
W
= (
F
cos
θ
)
s
(Equation 6.1) to determine
s
, we will need a value for the
angle
θ
between the frictional force and the displacement.
The frictional force points opposite to the
displacement, so
θ
= 180°.
b.
By using only the workenergy theorem it is not possible to determine the time
t
during which the
snowmobile coasts to a halt.
To determine
t
it is necessary to use the equations of kinematics.
We can use
these equations, if we assume that the acceleration during the coasting phase is constant.
The acceleration is
determined by the force of friction (assumed constant) and the mass of the snowmobile, according to Newton’s
second law.
For example, we can use
( )
1
2
0f
s
v vt
=
+
(Equation 2.7) to determine
t
once we know the
magnitude of the displacement
s
, which is the distance in which the snowmobile coasts to a halt.
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 Fall '08
 RICHARDSON, B
 Physics, Force, Work, Bungee

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