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friction is 0.350. Find the work
friction.
friction of 0.350 and a length of 1.50
required to move the mass a
m. Find (a) the total energy of the 52. In an Atwood s machine m
B
distance of 2.00 m.
block at A, (b) the velocity of the = 30.0 g, m = 50.0 g, h = 0.400 m,
A B
44. A 5.00-kg projectile is fired
block at B, (c) the energy lost along and h = 0.800 m. The machine
A
at an angle of 58.00 above the
path B-C, and (d) how high the starts from rest and mass m
A
horizontal with the initial velocity
acquires a velocity of 1.25 m/s as it
block rises along path C-D.
of 30.0 m/s. Find (a) the total
strikes the ground. Find the energy
energy of the projectile, (b) the total
lost due to friction in the bearings
energy in the vertical direction,
of the pulley.
(c) the total energy in the horizontal
7-26 Mechanics
*55. Modify problem 54 and find
the escape velocity for (a) the moon,
(b) Mars, and (c) Jupiter.
*56. The entire Atwood s
machine shown is allowed to go into
free-fall. Find the velocity of m and
1
m when the entire system has
2
fallen 1.00 m.
Diagram for problem 58.
*59. A 1.50-kg block moves
along a smooth horizontal surface
at 2.00 m/s. It then encounters a
smooth inclined plane that makes
Diagram for problem 52.
an angle of 53.00 with the
horizontal. How far up the incline
*53. What is the total energy of
will the block move before coming to
the Atwood s machine in the
rest?
position shown in the diagram? If
the blocks are released and m falls
1
through a distance of 1.00 m, what
is the kinetic and potential energy
of each block, and what are their
velocities?
Diagram for problem 56.
*57. A 1.50-kg block moves
along a smooth horizontal surface
Diagram for problem 59.
at 2.00 m/s. The horizontal surface
is at a height h above the ground.
*60. Repeat problem 59, but in
The block then slides down a rough
this case the inclined plane is rough
hill, 20.0 m long, that makes an
and the coefficient of kinetic friction
angle of 30.00 with the horizontal.
between the block and the plane is
The coefficient of kinetic friction
0.400.
between the block and the hill is
*61. In the diagram mass m is
1
0.600. How far down the hill will
located at the top of a rough
the block move before coming to
inclined plane that has a length l =
1
rest?
Diagram for problem 53.
0.500 m. m = 0.500 kg, m = 0.200
1 2
kg, µ = 0.500, µ = 0.300, ¸ =
k1 k2
*54. The gravitational potential
50.00, and Æ = 50.00. (a) Find the
energy of a mass m with respect to
total energy of the system in the
infinity is given by
position shown. (b) The system is
released from rest. Find the work
PE = -Gm m
E
done for block 1 to overcome friction
r
as it slides down the plane. (c) Find
the work done for block 2 to
where G is the universal Diagram for problem 57.
overcome friction as it slides up the
gravitational constant, m is the
E
plane. (d) Find the potential energy
mass of the earth, and r is the *58. At what point above the
of block 2 when it arrives at the top
distance from the center of the ground must a car be released such
of the plane. (e) Find the velocity of
earth to the mass m. Find the that when it rolls down the track
block 1 as it reaches the bottom of
escape velocity of a spaceship from and into the circular loop it will be
the plane. (f) Find the kinetic
the earth. (The escape velocity is going fast enough to make it
energy of each block at the end of
the necessary velocity to remove a completely around the loop? The
their travel.
body from the gravitational radius of the circular loop is R.
attraction of the earth.)
Chapter 7 Energy and Its Conservation 7-27
energy PE (relative to the ground), energy of mass 1, and (i) the kinetic
its kinetic energy KE, and its total energy of mass 2. (j) When mass 1
energy E for the first 10.0 s of hits the ground, find the speed of
tot
flight. Plot a graph of each energy each mass.
as a function of time. 66. General motion. Consider
64. Atwood s machine. Consider the general case of motion shown in
the general motion in an Atwood s the diagram with mass m initially
A
machine such as the one shown in located at the top of a rough
the diagram of problem 27; m = inclined plane of length l , and
A A
Diagram for problem 61.
0.650 kg and is at a height h = 2.55 mass m is at the bottom of the
A B
m above the reference plane and second plane; x is the distance
A
*62. If a constant force acting
mass m = 0.420 kg is at a height from the mass A to the bottom of
B
on a body is plotted against the
h = 0.400 m. If the system starts the plane. Let m = 0.750 kg, m =
B A B
displacement of the body from x to
1
from rest, find (a) the initial 0.250 kg, l = 0.550 m, ¸ = 40.00, Æ =
A
x , as shown in the diagram, then
2
potential energy of mass A, (b) the 30.00, µ = 0.400, µ = 0.300, and
kA kB
the work done is given by
initial potential energy of mass B, x = 0.200 m. When x = 0.200 m,
A A
and (c) the total energy of the find (a) the initial total energy of
W = F(x - x )
2 1
system. When m has fallen a the system, (b) the distance block B
A
= Area under the curve
distance y = 0.75 m, find (d) the has moved, (c) the potential energy
A
potential energy of mass A, (e) the of mass A, (d) the potential energy
Show that this concept can be
potential energy of mass B, (f) the of mass B, (e) the energy lost due to
extended to cover the case of a
speed of each mass at that point, friction for block A, (f) the energy
variable force, and hence find the
(g) the kinetic energy of mass A, lost due to friction for block B,
work done for the variable force, F
and (h) the kinetic energy of mass (g) the velocity of each block, (h) the
= kx, where k = 2.00 N/m as the
B. (i) When mass A hits the ground, kinetic energy of mass A, and (i) the
body is displaced from x to x .
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