Question

a.) Calculate the mass of a planet if the gravity (g) of the planet is 5.35 m/sec/sec

b.) Calculate the escape velocit of a satellite launched from the surface of Mars, Mass of the planet = 6.41693x10²³ kg and the radius of the planet = 3.39x10⁶ m.

c.) A rotating whell requires 3 sec. to rotate 37 revolutions, it's angular velocity at the end of 3 sec is 98 rad/sec calulate constant angulat acceleration of the wheel in rads/sec/sec

d.) A 75 kg person is rotating in the wheel of radius 15 m. Calculate his speed at the highest point, at the lowest point and the normal force he feels at the lowest point

Answer 1

a) we know, g = G*M/R^2

to find M, we need to know R

b) escape speed on a planet,

ve = sqrt(2*G*M/R)

= sqrt(2*6.67*10^-11*6.41693*10^23/(3.39*10^6))

= 5025 m/s

c) let wo is the initial angular velocity and alfa is the angular acceleration of the wheel.

use, theta = wo*t + 0.5*alfa*t^2

37*2*pi = wo*3 + 0.5*alfa*3^2 -----(1)

alfa = (wf - wi)/t

alfa = (98 - wo)/3 -----(2)

on solving the above two equation we get

alfa = 13.7 rad/s^2

d) at heighest point, V_min = sqrt(g*R)

= sqrt(9.8*15)

= 12.1 m/s

at lowest point, v = sqrt(5*g*R)

= sqrt(5*9.8*15)

= 27.1 m/s

at lowest point, Fnet = N - m*g

m*a_rad = N - m*g

N = m*g + m*a_rad

= m*g + m*v^2/R

= 75*9.8 + 75*27.1^2/15

= 4407 N