CHAPTER 6 HOMEWORK
1. (p.151 Ex.6) Calculate the effective value of g, the acceleration of gravity, qt (a) 3200m, and (b) 3200km, above the Earth's surface.
2. (p.151 Ex.9) Four masses are arranged as shown in Fig. 6-22. Determine the x and y components of the gravitational force on the mass at the origin (m). Write the force in vector notation (i, j).
3. (p.152 Ex. 23) What will a spring scale read for the weight of a 56-kg woman in an elevator that moves (a) with constant speed upward of 3.0m/s. (b) with constant speed downward of 3.0m/s, (c) with upward acceleration of 0.33g, and (e) in free fall?
4. (p.152 Ex.37) Our Sun rotates about the center of the Galaxy (M » 4 x 1041kg) at a distance of about 3 x 104 light years (1ly = 3 x 108m/s x 3.16 x 107s/y.) What is the period of our orbital motion about the center of the Galaxy?
5. (p.153 Ex.44) What is the magnitude and direction of the gravitational field midway between the Earth and Moon? Ignore effects of the Sun.
*6. (p.151 Ex.15)
(a) Use the binomial expansion
(1 + x )n = 1 + nx + [n(n - 1)/2]x2 + . . .
to show that the value of g is altered by approximately
Dg » -2g(Dr/rE)
at a height Dr above the Earth's surface, where rE is the radius of the Earth, as long as Dr << rE. (b) What is the meaning of the minus sign in this relation? (c) Use this result to compute the effective value of g at 100km above the Earth's surface. Compare to a direct use of Eq. 6-1.
*7. (p.152 Ex.32) An inclined plane, fixed to the inside of an elevator, makes a 30° angle with the floor, A mass m slides on the plane without friction. What is its acceleration relative to the plane if the elevator (a) accelerates upward at 0.50g, (b) accelerates downward at 0.50g, (c) falls freely, or (d) moves upward at constant speed?