Classical Mechanics - Curved Trajectory

The curvature of Mars is such that its surface drops a vertical distance of 2.0 meters for every 3600 meters tangent to the surface. In addition, the gravitational acceleration near its surface is 0.4 times that near the surface of Earth. What is the speed a golf ball would need to orbit Mars near the surface, ignoring the effects of air resistance?

A. 0.9 km/s
B. 1.8 km/s
C. 3.6 km/s
D. 4.5 km/s
E. 5.4 km/s

(GR9677 #22)

Solution:

y = ½ g_marst²

v_x = x/t 

Given:
y = 2
g_mars = 0.4 g 
x = 3600

2 = ½(0.4)(10)(t)²
t = 1 s
v_x = 3600/1 = 3600 m/s = 3.6 km/s

Answer: C

Optics - Telescope

A simple telescope consists of two convex lenses, the objective and the eyepiece, which have a common focal point P, as shown in the figure above. If the focal length of the objective is 1.0 meter and the angular magnification of the telescope is 10, what is the optical path length between objective and eyepiece? 

A. 0.1 m
B. 0.9 m
C. 1.0 m
D. 1.1 m
E. 10 m

(GR9277 #22)

Solution:

Magnification of the telescope: M = f₀/ f_e

The optical path length between objective and eyepiece d =  f₀ +  f_e

f₀ = focal length of the objective
f_e = focal length of the eyepiece

Since M = 10,  f₀ = 1

f_e = f₀/M = 0.1

d =  f₀ +  f_e = 1 + 0.1 = 1.1 m

Answer: D

Special Relativity - Electromagnetic Field

Which of the following statements most accurately describes how an electromagnetic field behaves under a Lorentz transformation?

1. The electric field transforms completely into a magnetic field.
2. If initially there is only an electric field, after the transformation there maybe both an electric and magnetic field.
3. The electric field is unaltered.
4. The magnetic field is unaltered.
5. It cannot be determined unless a gauge transformation is also specified.

(GR8677 #22)

Solution:

see analysis: Electromagnetism and Relativity

Answer: A

Classical Mechanics - Satellite

An astronomer observes a very small moon orbiting a planet and measures the moon’s minimum and maximum distances from the planet’s center and the moon’s maximum orbital speed. Which of the following CANNOT be calculated from these measurements?

A. Mass of the moon
B. Mass of the planet
C. Minimum speed of the moon
D. Period of the orbit
E. Semimajor axis of the orbit

(GR0177 #22)

Solution:

Let m = mass of the moon and M = mass of the planet,

F_c = F_G

mv²/r   = GMm/r²

m cancels out so, there’s no way to calculate mass of the moon.

Answer: A