Physics 18 Spring 2011 Homework 3 Wednesday February ... - Faculty

Physics 18 Spring 2011
Homework 3
Wednesday February 2, 2011
Make sure your name is on your homework, and please box your final answer. Because
we will be giving partial credit, be sure to attempt all the problems, even if you don’t
finish them. The homework is due at the beginning of class on Wednesday, February
9th. Because the solutions will be posted immediately after class, no late homeworks can
be accepted! You are welcome to ask questions during the discussion session or during office
hours.
1. Astronauts in apparent weightlessness during their stay on the International Space
Station must carefully monitor their masses because significant loss of body mass is
known to cause serious medical problems. Give an example of how you might design
equipment to measure the mass of an astronaut on the orbiting space station.
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2. A net force of (6.0 N) î − (3.0 N) ˆj acts on a 1.5 kg object. Find the acceleration a.
What is the magnitude of the acceleration, a?
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3. Seat belts and air bags save lives by reducing the forces exerted on the driver and
passengers in an automobile collision. Cars are designed with a “crumple zone” in the
front of the car. In the event of an impact, the passenger compartment decelerates over
a distance of about 1 m as the front of the car crumples. An occupant restrained by
seat belts and air bags decelerates with the car. By contrast, an unrestrained occupant
keeps moving forward with no loss of speed (Newton’s first law!) until hitting the
dashboard or windshield. These are unyielding surfaces, and the unfortunate occupant
then decelerates over a distance of only about 5 mm.
(a) A 60 kg person is in a head-on collusion. The car’s speed at impact is 15 m/s.
Estimate the net force on the person if he or she is wearing a seat belt and if the
air bag deploys.
(b) Estimate the net force that ultimately stops the person if he or she is not restrained
by a seat belt or air bag.
(c) How do these two forces compare to the person’s weight?
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4. A 35.0-kg traffic light is supported by
two wires as in the figure. (a) Draw the
light’s free-body diagram and use it to
answer the following question qualitatively:
Is the tension in wire 2 greater
than or less than the tension in wire 1?
(b) Verify your answer by applying Newton’s
laws and solving for the two tensions.
4

5. A 65-kg student weights himself by
standing on a force scale mounted on a
skateboard that is rolling down an incline,
as shown in the figure. Assume there is no
friction so that the force exerted by the
incline on the skateboard is normal to the
incline. What is the reading on the scale
if θ = 30 ◦ ?
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6. A block of mass m slides across a frictionless
floor and then up a frictionless ramp.
The angle of the ramp θ and the speed of
the block before it starts up the ramp is
v0. The block will slide up to some height
h above the floor before stopping. Show
that h is independent of m and θ by deriving
an expression for h in terms of v0 and g.
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7. A block of mass m is being lifted vertically by a uniform rope of mass M and length
L. The rope is being pulled upward by a force applied to its top end, and the rope
and block are accelerating upward with an acceleration of magnitude a. Show that
the tension in the rope at a distance x (where x < L) above the block is given by
(a + g) [m + (x/L) M].
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8. The figure shows a 20-kg block sliding on
a 10-kg block. All surfaces are frictionless
and the pulley is massless and frictionless.
Find the acceleration of each block and
the tension in the string that connects the
blocks.
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9. A 2.0 kg block rests on a frictionless wedge
that has a 60 ◦ incline and an acceleration
a to the right such that the mass remains
stationary to the wedge. (a) Draw the
free-body diagram of the block and use
it to determine the magnitude of the
acceleration. (b) What would happen
if the wedge were given an acceleration
larger than this value? Smaller than this
value?
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10. Elvis Presley has supposedly been sighted
numerous times since his death on August
16, 1977. The following is a chart of
what Elvis’s weight would be if here were
sighted on the surfaces of other objects
in our solar system. Use the chart to
determine: (a) Elvis’s mass on Earth, (b)
Elvis’s mass on Pluto, and (c) the free-fall
acceleration on Mars. (d) Compare the
free-fall acceleration on Pluto to the
free-fall acceleration on the moon.
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Planet Elvis’s Weight (N)
Mercury 431
Venus 1031
Earth 1133
Mars 431
Jupiter 2880
Saturn 1222
Pluto 58
Moon 191