Planet X revolves around the Sun in a circular orbit of radius 130 times that of
ID: 3164304 • Letter: P
Question
Planet X revolves around the Sun in a circular orbit of radius 130 times that of Earth, The diameter of Planet X is one fourth Earth's diameter and the mass is twice Earth's. a. Calculate the year of Planet X. b. Calculate the acceleration due to gravity, g_x on the surface of Planet X (due to Planet X). c. Calculate the weight of a 70-kg astronaut on the surface of Planet X. d. Calculate the Sun's gravitational force acting on planet X. A 900-kg roller coaster starts from the top of a 50-m high hill (A) coasts for along the track, coming to rest at a height of 10 m (B). Assume a constant fractional on the roller coaster. A. Calculate the work done by the frictional force on the rollercoaster. b. Maintenance on the track eliminates the frictional force. Calculate the speed roller coaster at the 10-m height. A horizontal spring is compressed inside a spring gun by a distance of 10 cm equilibrium length. A 40-g ball is placed against the end of the spring, and the released giving the ball a speed of 10 m/s. a. Calculate the spring constant. B. Calculate the force exerted by the spring on the ball just before release. c. Calculate the work done by the spring on the ball when the spring is A force F = 10 N i + 25 N j + 34 N k acts on an object which moves through the d = 11 mi + 18 m k. a. Calculate the work done by the force. b Calculate the angle between F and d.Explanation / Answer
1. r = 130 R
R = orbit radius of earth around sun = 149.6 x 10^9 m
r = 1.945 x 10^13 m
For circular orbit aorund the sun,
G Ms m / r^2 = m w^2 r
w^2 = G Msun / r^3 = (6.67 x 10^-11) ( 1.99 x 10^30) / (1.945 x 10^13)^3
w = 1.343 x 10^-10 rad/s
T = 2pi / w = 4.677 x 10^10 sec
T(in earth days) = (4.667 x 10^10) / (24 x 3600)
1 year of given planet = 541363.65 earth days OR 1483.2 earth years
(B) gx = G m / Rp^2
Rp = 6371 x 10^3 m / 4 = 1592750 m
m = 2 x 5.972 x 10^24 kg
G = 6.67 x 10^-11
putting in
gx = 314.04 m/s^2
(C) W = m gx = 70 x 314.04 = 21982.8 N
(D) Fg = G M m / r^2
= (6.67 x 10^-11) (1.99 x 10^30) (2 x 5.972 x 10^24) / (1.945 x 10^13)^2
= 4.19 x 10^18 N