# Physics 1303,1403 - Spring 1997

# Homework Assignment #7

**Due:**

24 April (Sections 002 and 802)

25 April (Sections 001 and 801)

### READING

Chapters 13 and 14.
### QUESTIONS

Chapter 13 - 1, 4, 10, 11, 17, 19.

Chapter 14 - 1, 3, 5, 8, 9, 12, 13, 14, 19.
### PROBLEMS

Chapter 13 - 1, 5, 9, 10, 21, 25, 60.

Chapter 14 - Review Problem, 1, 5, 6, 11, 12, 15, 18, 19, 30, 33, 53, 55.
### ANSWERS

**Q 13-1)** 4A

**Q 13-4)**
- yes
- yes
- no

**Q 13-10)** If L is doubled, then T increases by sqrt(2).

If M is doubled, then T remains unchanged.

**Q 13-11)**
- period decreases
- period increases
- period remains unchanged

**Q 13-17)** to avoid destroying the bridge by resonance.

**Q 13-19)** shorten the length of the pendulum.

**Q 14-1)** order of magnitude: 10^{-7} newtons

**Q 14-3)** 10

**Q 14-5)** No.

**Q 14-8)** U = -2 K for a circular orbit. For a general elliptical
orbit, the absolute value of U is always greater than K, and U is
always negative. The total energy E=U+K is therefore always negative.

**Q 14-9)** F is always perpendicular to displacement in a circular
orbit. In an elliptical orbit, sometimes positive work is done (and
the particle speeds up), sometimes negative work is done (the particle
slows down), but the NET work done in one full revolution is zero.

**Q 14-12)** Speed is a maximum when the planet is closest to the Sun.
Speed is a minimum when the planet is farthest from the Sun.

**Q 14-13)** g_{X} = G M_{X}/R_{X}^{2}

**Q 14-14)** The gravitational force on m_{1} at the center of
the Earth is zero.
Equation 14-1 is correct if m_{2} is the mass "under"
m_{1}. That is, one discounts all the mass in the Earth
further from the center than m_{2}'s.

**Q 14-19)** The centripetal acceleration at the equator is about
0.003 of a "g". (0.034 m/s^{2})

**P 13-1)**
- f=1.50 Hz, T=0.667 s
- 4.00 m
- Pi rad = 3.1416 rad
- 2.83 m

**P 13-5)**
- v=13.9 cm/s, a=16.0 cm/s
^{2}
- v
_{max} = 16.0 cm/s at t=0.262 s
- a
_{max} = 32 cm/s^{2} at t=1.05 s

**P 13-9)**
- 0.542 kg
- 1.81 s
- 1.20 m/s
^{2}

**P 13-10)** 0.627 s

**P 13-21)**
- E increases by 4 times
- v
_{max} is doubled
- a
_{max} is doubled
- T is unchanged

**P 13-25)**
- 1.55 m
- 6.06 s

**P 13-60)**
- 0.50 m/s
- 0.0856 m

**P 14-Review)**
- sqrt(GM/R)
- 2 Pi sqrt(R
^{3} / GM)
- GmM / 2R
- - GmM / R
- sqrt(GM / g)
- 2 Pi (GM / g
^{3} )^{1/4}
- m/2 sqrt(gGM)
- - m sqrt(gGM)
- sqrt(2GM / R) this is sqrt(2) times faster than its orbital speed.

**P 14-1)**
- 3.46 x 10
^{8} m
- 3.34 x 10
^{-3} m/s^{2}

**P 14-5)** g = Gm / L^{2} [sqrt(2) + 1/2 ] toward the opposite
corner

**P 14-6)** g/16 = 0.613 m/s^{2}

**P 14-11)** M = 1.26 x 10^{32} kg = 63 solar masses for each star

**P 14-12)**
- 1024 m/s
- 0.0014 m = 1.4 mm = 1/20 inch

**P 14-15)** 1.9 x 10^{27} kg ( = 316 Earth masses)

**P 14-18)** 226 N

**P 14-19)** 89,800 km above THE SURFACE

**P 14-30)** 469 megajoules

**P 14-33)** Proof required (see review problem)

**P 14-53)** 313 rad/s = 3000 rpm (revolutions per minute)

**P 14-55)**
- v
_{1} = m_{2} sqrt[2G / d(m_{1}+m_{2})]
and
v_{2} = m_{1} sqrt[2G / d(m_{1}+m_{2})]

relative velocity = sqrt[2G(m_{1}+m_{2}) / d]
- K
_{1} = 1.07 x 10^{32} J and
K_{2} = 2.67 x 10^{31} J

Please report any corrections to
Professor Scalise.

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