Problems
289
ter of the string fixed to represent the tree branch, and re-
produce a model of the motions of George and the gorilla.
What changes in your analysis will make it apply to this situ-
ation? What If? Assume the magnet is strong, so that it no-
ticeably attracts the screw over a distance of a few centime-
ters. Then the screw will be moving faster just before it
sticks to the magnet. Does this make a difference?
64.
A cannon is rigidly attached to a carriage, which can move
along horizontal rails but is connected to a post by a large
spring, initially unstretched and with force constant k !
2.00 * 10
4
N/m, as in Figure P9.64. The cannon fires a
200-kg projectile at a velocity of 125 m/s directed 45.0°
above the horizontal. (a) If the mass of the cannon and its
carriage is 5 000 kg, find the recoil speed of the cannon.
(b) Determine the maximum extension of the spring.
(c) Find the maximum force the spring exerts on the car-
riage. (d) Consider the system consisting of the cannon,
carriage, and shell. Is the momentum of this system con-
served during the firing? Why or why not?
through the relation
What numerical value does she obtain for v
1
A
based on
her measured values of x ! 257 cm and y ! 85.3 cm?
What factors might account for the difference in this
value compared to that obtained in part (a)?
66.
Small ice cubes, each of mass 5.00 g, slide down a friction-
less track in a steady stream, as shown in Figure P9.66.
Starting from rest, each cube moves down through a net
vertical distance of 1.50 m and leaves the bottom end of
the track at an angle of 40.0° above the horizontal. At the
highest point of its subsequent trajectory, the cube strikes
a vertical wall and rebounds with half the speed it had
upon impact. If 10.0 cubes strike the wall per second, what
average force is exerted on the wall?
v
1
A
!
x
√
2y/g
y
v
1
A
x
Figure P9.65
40.0
°
1.50 m
Figure P9.66
v
5.00 cm
400 m/s
Figure P9.67
65.
A student performs a ballistic pendulum experiment using
an apparatus similar to that shown in Figure 9.11b. She ob-
tains the following average data: h ! 8.68 cm, m
1
!
68.8 g,
and m
2
!
263 g. The symbols refer to the quantities in Fig-
ure 9.11a. (a) Determine the initial speed v
1
A
of the pro-
jectile. (b) The second part of her experiment is to obtain
v
1
A
by firing the same projectile horizontally (with the pen-
dulum removed from the path), by measuring its final hor-
izontal position x and distance of fall y (Fig. P9.65). Show
that the initial speed of the projectile is related to x and y
45.0
°
Figure P9.64
A 5.00-g bullet moving with an initial speed of 400 m/s is
fired into and passes through a 1.00-kg block, as in Figure
P9.67. The block, initially at rest on a frictionless, horizon-
tal surface, is connected to a spring with force constant
900 N/m. If the block moves 5.00 cm to the right after im-
pact, find (a) the speed at which the bullet emerges from
the block and (b) the mechanical energy converted into
internal energy in the collision.
67.
68.
Consider as a system the Sun with the Earth in a circular
orbit around it. Find the magnitude of the change in
the velocity of the Sun relative to the center of mass of the