Exam #1 W2000

1. A 1.40 kg rock is launched from the surface of the Moon straight upwards. The rock is observed to rise to a height of 86.0 km above the surface of the Moon. The Moon’s mass is 7.349x10 ²² kg and its mean radius is 1738 km.

(A) What is the rock’s downward acceleration when it reaches its maximum separation from the Moon?
Ans:{1.47 m/s ²}
(B) What is the total mechanical energy of the rock relative to infinity when it was launched?
Ans:{-3.76 MJ}
(C) With what velocity was the rock launched?
Ans:{516 m/s}

2. A 950 kg satellite in orbit about the Moon takes 11.0 hours to orbit once. The Moon’s mass is 7.349x10 ²² kg and its mean radius is 1738 km. If the satellite’s orbit has an eccentricity of .380:

(A) What the average distance of the satellite from the center of the Moon, i.e., what is its semimajor axis?
Ans:{5800 km}
(B) What is the force of gravity of the Moon on the satellite when it is at closest distance to the Moon?
Ans:{361 N}
(C) What is the slowest the satellite will move in its orbit about the Moon?
Ans:{616 m/s}

3. A particle oscillates 270 times a minute with an amplitude of 61.0 cm. If the oscillations can be approximated by simple harmonic motion with an initial phase angle of +130.0 ^o for the solution:

(A) what is the distance of the particle from the center of oscillation at the start?
Ans:{46.7 cm}
(B) what is the angular frequency in rad/sec of the oscillating particle?
Ans:{28.3 rad/s}
(C) what is the velocity of the particle when it 7/10 of the way through its cycle?
Ans:{16.0 m/s}

4. A 380 g mass oscillates on the end of a massless horizontal spring on a frictionless surface. The maximum kinetic energy and maximum acceleration of the mass is 4.70 J and 110 m/s ².

(A) What is the maximum speed of the mass?
Ans:{4.97 m/s}
(B) How long does it take the mass to oscillate back and forth once?
Ans:{.284 s}
(C) What is the magnitude of the spring constant k of the spring?
Ans:{186 N/m}

Exam #1 Spring 2000

(A) What is the maximum height above the Moon will the rock reach?
Ans:{117 km}

(B) What is the rock’s downward acceleration when it reaches its maximum separation from the Moon?
Ans:{1.42 m/s ²}

(C) With what velocity was the rock launched?
Ans:{598 m/s}

(A) How long will it take for the satellite to travel from its closest approach to the Moon to its maximum distance from the Moon?
Ans:{23,000 s or 6.38 hr}

(B) What is the force of gravity of the Moon on the satellite when it is at maximum distance from the Moon?
Ans:{63.5 N}

(C) What is the fastest the satellite will move in its orbit about the Moon?
Ans:{1.40 km/s}

3. A simple pendulum is constructed with a 450 gram bob and a cord with a length of 1.30 meters. The phase angle of the pendulum’s motion is 41.0 ^O for the SHM solution q( t) = q _max sin(w t +f). If the maximum speed of the bob is 16.5 cm/s.

(A) How long will it take to make one complete oscillation?
Ans:{2.29 s}

(B) With what velocity did the pendulum start at time t = 0?
Ans:{12.5 cm/s}

(C) What is the maximum angle that the pendulum makes with the vertical in degrees ?
Ans:{2.65 ⁰}

(A) How long will it take the block to make one complete oscillation?
Ans:{33.4 ms}

(B) What is the value of the spring constant k?
Ans:{17400N/m}

(C) What is the velocity of the block when the spring is stretch to 8.80 mm?
Ans:{2.74 m/s}