169
.
Flift
Fthrust
Problem 9.
Problem 10.
.
.
6. A skier of mass m is coasting down a slope inclined at an angle
.
compared to horizontal. Assume for simplicity that the treatment of
kinetic friction given in chapter 5 is appropriate here, although a soft and
wet surface actually behaves a little differently. The coefficient of kinetic
friction acting between the skis and the snow is
µ
k
, and in addition the
skier experiences an air friction force of magnitude bv
2
, where b is a
constant. (a) Find the maximum speed that the skier will attain, in terms
of the variables m,
.
,
µ
k
, and b. (b) For angles below a certain minimum
angle
.
min
, the equation gives a result that is not mathematically meaning-
ful. Find an equation for
.
min
, and give a physical explanation of what is
happening for
.
<
.
min
.
7
.
. A gun is aimed horizontally to the west, and fired at t=0. The bullet's
position vector as a function of time is
r=bx
+cty
+dt
2
z
, where b, c,
and d are constants. (a) What units would b, c, and d need to have for the
equation to make sense. (b) Find the bullet's velocity and acceleration as
functions of time. (c) Give physical interpretations of b, c, d,
x
,
y
, and
z
.
8 S. Annie Oakley, riding north on horseback at 30 mi/hr, shoots her rifle,
aiming horizontally and to the northeast. The muzzle speed of the rifle is
140 mi/hr. When the bullet hits a defenseless fuzzy animal, what is its
speed of impact. Neglect air resistance, and ignore the vertical motion of
the bullet.
9 S. A cargo plane has taken off from a tiny airstrip in the Andes, and is
climbing at constant speed, at an angle of
.
=17
°
with respect to horizon-
tal. Its engines supply a thrust of F
thrust
=200 kN, and the lift from its
wings is F
lift
=654 kN. Assume that air resistance (drag) is negligible, so the
only forces acting are thrust, lift, and weight. What is its mass, in kg.
10 S. A wagon is being pulled at constant speed up a slope
.
by a rope
that makes an angle
.
with the vertical. (a) Assuming negligible friction,
show that the tension in the rope is given by the equation
F
T
=sin
.
sin
.
+
.
F
W
,
where F
W
is the weight force acting on the wagon. (b) Interpret this
equation in the special cases of
.
=0 and
.
=180
°
-
.
.
11 S. The angle of repose is the maximum slope on which an object will
not slide. On airless, geologically inert bodies like the moon or an asteroid,
the only thing that determines whether dust or rubble will stay on a slope
is whether the slope is less steep than the angle of repose. (a) Find an
equation for the angle of repose, deciding for yourself what are the
relevant variables. (b) On an asteroid, where g can be thousands of times
lower than on Earth, would rubble be able to lie at a steeper angle of
repose.
Homework Problems