- Call us if you have any questions:
- +61 (0) 383 766 284

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 .

3. RotationalMotion

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

the column.

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?

Its speed.

Its pressure

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

L/min?

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°)