Question

1. (a) Determine the amount of work (in joules) that must be done on a 100 kg payload to elevate it to a height of 1005 km above the Earth's surface.
______MJ
(b) Determine the amount of additional work that is required to put the payload into circular orbit at this elevation.
_______ J

2. A vertical spring stretches 4.0 cm when a 12-g object is hung from it. The object is replaced with a block of mass 20 g that oscillates up and down in simple harmonic motion. Calculate the period of motion.

_______s

Answer 1

1a) amount of work done is W = m*g*h = (100*9.8*1005*1000) = 985*10^6 J = 985 MJ

b) v = sqrt(GM/R) = sqrt((6.67*10^-7*5.98*10^24)/((6.38*10^6)+(1.005*10^6))) = 7.35*10^5 m/sec

Work done is W = m*g*h + 0.5*m*v^2 = 985*10^6 + (0.5*100*7.35*10^5) = 1.02*10^9 J

additional work is 36.75 MJ

2) spring constant is k = F/x = (m*g)/x = (12*10^-3*9.8)/0.04 = 2.94 N/m

then T = 2*pi/w

w = sqrt(k/m) = sqrt(2.94/(20*10^-3)) = 12.12

then T = 2*pi/w = 2*3.142/12.12 = 0.52 sec