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Physics 21 First Semester

Introductory Physics Problem Set 2 A.Y. 2019 - 2020

Consult ONLY your professor if you have questions regarding the problem set. Complete
solutions must be shown to merit full points. Write solutions in sheets of yellow pad. Start
a new page for each item and there must be no solutions at the back of the papers.
DEADLINE: November 23, 1:00 p.m.

Each item is worth 2 points.

1. In the treatment of spine injuries, it is often necessary to provide tension along the
spinal column to stretch the backbone. One device for doing this is the Stryker frame
(see figure below). A weight W is attached to the patient (sometimes around a neck
collar), and friction between the person’s body and the bed prevents sliding. (a) If the
coefficient of static friction between a 78.5-kg patient’s body and the bed is 0.75, what
is the maximum traction force along the spinal column that W can provide without
causing the patient to slide? (b) Under the conditions of maximum traction, what is
the tension in each cable attached to the neck collar?

Figure 1: Example of Stryker frame

2. A man pushes on a piano with mass 180 kg; it slides at constant velocity down a ramp
that is inclined at 19.0◦ above the horizontal floor. Neglect any friction acting on the
piano. Calculate the magnitude of the force applied by the man if he pushes (a) parallel
to the incline and (b) parallel to the floor.

3. Two uniform spheres, each with mass M and radius R, touch each other. What is the
magnitude of their gravitational force of attraction?

4. On October 15, 2001, a planet was discovered orbiting around the star HD 68988. Its
orbital distance was measured to be 10.5 million kilometers from the center of the star,
and its orbital period was estimated at 6.3 days. What is the mass of HD 68988?
Express your answer in kilograms and in terms of our sun’s mass.

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Physics 21 First Semester
Introductory Physics Problem Set 2 A.Y. 2019 - 2020

5. Adult cheetahs, the fastest of the great cats, have a mass of about 70 kg and have been
clocked to run at up to 72 mi/h 132 m/s2 . (a) How many joules of kinetic energy does
such a swift cheetah have? (b) By what factor would its kinetic energy change if its
speed were doubled?

6. A force parallel to the x-axis acts on a particle moving along the x-axis. This force
produces potential energy U (x) given by U (x) = ax4 , where a = 0.630 J/m4 . What is
the force (magnitude and direction) when the particle is at x = -0.800 m?

7. A 15.0-kg fish swimming at 1.10 m¿s suddenly gobbles up a 4.50-kg fish that is initially
stationary. Ignore any drag effects of the water. (a) Find the speed of the large fish
just after it eats the small one. (b) How much mechanical energy was dissipated during
this meal?

8. If the force on the tympanic membrane (eardrum) increases by about 1.5 N above the
force from atmospheric pressure, the membrane can be damaged. When you go scuba
diving in the ocean, below what depth could damage to your eardrum start to occur?
The eardrum is typically 8.2 mm in diameter.

9. A sealed tank containing seawater to a height of 11.0 m also contains air above the
water at a gauge pressure of 3.00 atm. Water flows out from the bottom through a
small hole. How fast is this water moving?

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