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1.
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Show that the work done on an object
equals (a) the product of the displacement and the component
of the force in the direction of the displacement or (b) the
product of the force and the component of the displacement
in the direction of the force.
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2.
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A box rests on a horizontal, frictionless
surface. A girl pushes on the box with a force of 18 N to
the right and a boy pushes on the box with a force of 12 N
to the left. The box moves 4.0 m to the right. Find the work
done by (a) the girl, (b) the boy, and (c) the net force.
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3.
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You support an object and move it to
the right with a constant velocity. You exert a force F
on it (Fig. 1 below) to oppose the gravitational attraction
mg of the earth for the object. If you do not raise
the object or increase its velocity, there is no increase
in the object’s potential energy or in its kinetic energy.
Do you do work on the object?
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4.
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An object attached to a string, fixed
at one end, lies on a horizontal, frictionless surface. The
object is given an initial velocity v and moves in a circle
with uniform circular motion. Does the tension in the string
do work on the object?
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5.
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As illustrated in Fig. 2 below, an object
of mass m = 2.0 kg is pulled along a surface by a horizontal
force F of 12 N to the right a distance s of 4.0 m. The coefficient
of friction between the object and the surface is 0.5. Find
the work done by (a) F, (b) the normal force FN,
(c) the weight mg of the object, (d) the frictional
force f, (e) the net force.
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6.
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A raindrop (m = 3.35 x 10-5
kg) falls vertically at constant speed under the forces of
gravity and air resistance. In falling through 100 m, what
is the work done by (a) gravity and (b) air resistance?
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7.
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A 52-kg skier moves down a slope at a
speed of 14.0 m/s (31.3 mph). Determine the kinetic energy
of the skier.
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8.
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An object, initially at rest, is pulled
up an incline that makes an angle of 370
with the horizontal by a force F = 30 N parallel to the incline.
The mass of the object is 2.0 kg and the coefficient of friction
between the object and the surface is 0.5. The object moves
up the incline a distance s = 4.0 m. Find (a) the frictional
force, (b) the work done by F, (c) the work done by the normal
force, (d) the work done by the weight of the object, (e)
the work done by friction, (f) the work done by the net force
and (g) the velocity of the object after it has moved 4.0
m.
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9.
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A 2.0-kg object is pushed along a horizontal
surface a distance s = 4.0 m by a force F = 30 N to the right
and down at an angle of 370 to the
horizontal. The coefficient of friction between the object
and the surface is 0.50. Find (a) the frictional force, (b)
the work done by the frictional force, (c) the work done by
force F, (d) the work done by the normal force FN,
(e) the work done by the weight of the object, (f) the net
work done on the object, and (g) the speed of the object after
it moves through s = 4.0 m if its initial speed = 0.
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10.
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A constant force of 10 N is exerted to
lift a l.0-kg mass a vertical height of 1.0 m. Find (a) the
work done by the person, (b) the work done by the gravitational
force, (c) the increase in its gravitational energy, and (d)
the increase in its kinetic energy. Take g = 10 m/s2.
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11.
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Repeat Problem #10 for a constant force
of 12 N.
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12.
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A box of mass 12 kg slides at a speed
of 10 m/s across a smooth level floor, where it enters a rough
portion 3.0 m in length. In the rough portion, the box experiences
a horizontal frictional force of 72 N. (a) How much work is
done by the frictional force? (b) What is the velocity of
the box when it leaves the rough surface? (c) What length
of rough surface brings the box completely to rest? Take g
= 10 m/s2.
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13.
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(a) How much work is required to push
a 2.0-kg object up a frictionless inclined plane whose length
is 2.0 m and whose height is 1.0 m, if the velocity of the
object remains constant? (b) How much work is required to
push the object up the plane while increasing its velocity
from zero to 3.0 m/s? (c) How much work is required to push
the object up the plane at a constant speed if there is a
frictional force of 3.0 N between the object and the plane?
Take g = 10 m/s2.
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14.
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A block of mass 1.0 kg is placed at the
top of an incline of length 125 m and height 62.5 m. The plane
has a rough surface. When the block arrives at the bottom
of the plane it has a velocity of 25 m/s. What is the magnitude
of the constant frictional force acting on the block? Take
g = 10m/s2.
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15.
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Assume that the total energy of an electron
bound to a proton in the hydrogen atom is -21.7 x 10-19
J. What is the kinetic energy of the electron (we assume
the proton is at rest) when the potential energy of the atom
is -43.4 x 10-19 J?
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16.
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A 2000-kg car is at rest on a level frictionless
track. A constant force acts on it for one-half second, after
which the car is moving with a speed of 0.20 m/s. Find (a)
the magnitude of the force, (b) the kinetic energy of the
car, (c) the work done on the car, and (d) the displacement
of the car.
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17.
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Find (a) i ·
i, (b) i · j
= j · i, (c)
j · j, (d)
the work done if the force F = 20 N j and the
displacement s = 4 m i and (e) the work done
if the force F = (3i + 4j)N and the displacement
s = (2i - 2j) m.
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18.
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An object of mass m = 2.0 kg is released
from rest at the top of a frictionless incline of height 3
m and length 5 m. Taking g = 10 m/s2,
use energy considerations to find the velocity of the object
at the bottom of the incline.
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19.
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Repeat #29 when µk between
the object and the plane is 1/4.
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20.
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Figure 3 below is a plot of the potential
energy U of a freely falling object as a function of the height
y above the ground. E = 16.0 J (shown by the dashed horizontal
line) is the total mechanical energy of the object. Find (a)
the potential energy and (b) the kinetic energy of the object
for y = 0.75 m. Find (c) mass of the object and (d) v when
y = 0.75 m. Take g = 10 m/s2.
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21.
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A small block of mass m slides along
the frictionless loop-the-loop shown in Fig. 4 below. Find
(a) the minimum height h above the bottom of the track which
you must release the block so that it will not leave the track
at the top of the hoop and (b) the force of the track on the
sphere at P in Fig. 4 when it is released from the height
h found in (a). Take g = 10 m/s2.
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22.
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In Fig. 5 below, the first block has
a mass m1 = 2.0 kg and the second block has m2
= 4.0 kg. The pulley and string are massless. There is no
friction in the pulley, but the coefficient of kinetic friction
between the first block and the incline is µk
= 0.55. The blocks are released from rest. Use energy considerations
to find the speed of the two blocks when the second block
has moved down 2.5 m. Take g = 10 m/s2.
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23.
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A very light rod of length L has a ball
of mass m attached to one end. The other end rotates about
a pivot without friction. The system rotates in a vertical
circle starting at position A in Fig. 6 below with downward
velocity vo. When the ball
reaches D, it stops and swings back down in a clockwise direction.
Find (a) an expression for vo in
terms of L, m, and g and (b) the tension in the rod at position
B. A little sand gets into the pivot and then the ball only
reaches C when launched from A. Find (c) the work done by
friction during the motion from A to C and (d) how much total
work is done by friction when the ball finally comes to rest
at B after oscillating back and forth a few times.
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