Solution: Some of the energy would be transmitted in the form of heat to the table instead of the water, and the temperature of the water would not rise as much.
Question: This figure illustrates Joule's classic experiment
demonstrating the equivalence of work and heat. The paddles inside the cylinder
are connected via pulleys to a weight (yellow). As the weight falls, the paddle
wheel turns, and the water's temperature goes up. In energy terms, the
gravitational potential energy lost by the weight shows up as thermal energy in
the water, and the rise in temperature can be easily predicted given the heat
capacity of the water. If the weight falls rapidly and hits the table on which
the apparatus is resting, what goes wrong with the measurement?
Solution: Some of the energy would be transmitted in the form of heat to the
table instead of the water, and the temperature of the water would not rise as
much.
Sample problem: In an emergency, the passengers on an airplane slide
down a curved escape ramp to safety (the figure below). The ramp has a 10.0-m
radius of curvature and the passengers exit the plane 2.5 above the ground.
Assuming a frictionless slide, what is the apparent weight of a 72-kg passenger
near the bottom of the ramp?
Solution:
Sample problem: A 60-kg young Tarzan ties a rope to a tree limb and
uses it to swing into the water below. If the rope is 6 m long and Tarzan is
initially holding the rope taut at the same vertical level as the knot, what minimum
tension should it be able to withstand?
Solution: Note that, in this example, the drop in height (h) equals the
length of the rope (r). The maximum tension occurs at the bottom, where the velocity
and thus the centripetal force is greatest.
Sample problem: A child is skiing down a virtually frictionless
snow-clad hill. At the bottom of the hill, the child encounters a section of
unpacked snow which causes him to slow down and eventually stop. If the height
of the hill is 52 m and the coefficient
of kinetic friction between skis and the unpacked snow is 0.1, how long does it
take this child to stop? What is the stopping distance?
Solution:
Sample problem: A boy exerts a force of 11 N at 29º above the
horizontal on a 6.4 kg sled. Find the work done by the boy and the final speed
of the sled after it moves 2 m, assuming the sled starts with an initial speed
of 0.5 m/s and slides horizontally without friction.
Solution: Note that only the horizontal component does work on the sled
(which is moving horizontally). The vertical component simply reduces the normal
forces and thus the force of friction.
Sample problem: In the movie Armageddon, a crew of hard-boiled oil
drillers rendezvous with a menacing asteroid just as it passes in the orbit of
the Moon on its way toward the Earth. Assuming the asteroid starts from rest at
infinity, find its speed when it passes the Moon’s orbit, which has a radius
equal to 60RE.
Solution: The loss of gravitational potential energy (i.e., the
work done by the force of gravity) shows up in an increase in the kinetic
energy. Note that mgh is the work done against a constant force mg over a
distance h. When the force is not constant, the more general expression for the
work against gravity must be used.
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