Assignment #1: (Due Feb. 7)
Vectors vs. Pseudovectors
Show that the vector cross product of two pseudovectors is a pseudovector and that the vector cross product of a vector and a pseudovector is a vector. (Recall that a pseudovector is defined as the result of the cross product of two vectors.)
Consider the effect that a mirror operation on the components of a vector. Describe any differences between a vector and a pseudovector under the mirror operation.
Velocity and Acceleration
a. A body moving in a straight line with uniform acceleration passes two consecutive equal space each of width w in times t and t . Show that the acceleration is: 2wt1 t2 .
a. A reel of thread whose rim and spindle are of radius a and b respectively rests of a rough horizontal table. The loose end of the thread passes under the spindle and leads off at an angle
above the horizontal 12 . Show that the least tension in it will in general wind or unwind the tread according as is less or greater than a certain value. When has this critical
value show that there will be no motion unless the tension exceeds another critical value.
4. Orbital Motion
A mass approaches the solar system with a velocity v0 and if it had not been attracted toward
the sun it would have missed the sun by a distance b . Use the laws of conservation of energy and angular momentum and the law of gravitation to compute its closest distance of approach
a to the sun. Neglect the gravitational attractions of the planets and assume the sun is fixed.
Note the answer is a b2 b2 1/ 2 b where b GM with M being the mass of the sun.
1 2 tt t t 1212
0 0 0 v02
1. Would the mass
density of an object be the same if the object were on the moon rather than on
the earth? Would the weight be the same?
2. A steel column in a building has a
cross-sectional area of?3500 cm?^2 and supports a
weight of 2.5 x?10?^5 N. Find the stress of
3. Each vertical steel column of an office
building supports a weight of 1.30 x?10?^5 N and is
compressed to 5.90 x?10?^(-3) cm.
Find the compression in each column if a weight
of 5.50 x?10?^5 N is supported.
If the compression of each steel column is
0.0710 cm, what weight is supported by each column?4. The specific gravity of
an unknown substance is 0.80.Will it float on or sink in gasoline?5. In a deep
dive, a whale is appreciably compressed by the pressure of the surrounding
water. What happens to the whale’s density?6. Would it be slightly more
difficult to draw soda through a straw at sea level that on top of a very high
mountain? Explain.7. When a steadily flowing gas flows from a larger diameter
pipe to a smaller diameter pipe, what happens to the following?
The spacing between its streamlines8. The large
piston in a hydraulic lift has a radius of?250 cm?^2. What force must be
applied to the small piston with a radius of?25 cm?^2 in order to raise a car
of mass 1500 kg?9. Water flows through a 13.0 cm diameter fire hose at a rate
of 4.53 m/s.
What is the rate of flow through the hose in
How many liters pass through the hose in 25.0
min?10. Suppose you cut a small gap in a metal ring. If you heat the ring, will
the gap become wider or narrower?11. The temperature of a 1 m long aluminum rod
is 20° C. If the temperature is increased to 70° C what is the length of the
rod if the coefficient of linear expansion for aluminum is 2.3x?10?^(-5)/° C.12. The specific
heat capacity of copper is 0.092 C/gm/° C. Show that the amount of heat needed
to raise the temperature of a 10-gram piece of copper from 0° C to 100° C is 92
calories. How does this compare with the heat needed to raise the temperature
of the same mass of water through the same difference?13. A liter of water is
used to cool electronics. If 1,000 Joules of heat is given off by the
electronics, by what temperature does the water increase? One liter of water
has a mass of 1 kg and a specific heat of 4.184 Joules/(g C°)