Question

4. a. If a 75 kg man runs around a vertical loop of radius 3 m, find the minimum speed he has to maintain to make this happen and the normal force at this speed.

b. If this same man is now placed in orbit around the Earth at an altitude of 300 km, find the required speed for this to be a stable, circular orbit.

Answer 1

a. let the speed be v ,

Then normal force be N =. mg = 75 x 9.81= 735.75N

Let v be the minimum speed then mv^2/r= N

Here r = radius of orbit , then

75 x v^2 /3= 735.75

Henc v = 5.42 m/s

b. Let speed be v' then for stable circular motion force by gravity should be equal to centrifugal force ,

GmM / r^2 = mv^2 / r

Here r = 6371 + 300 = 6671km = 6671000 m

Here 6371 is radius of earth then , M is the mass of earth ,m is the mass of satellite , G is the gravitational constant

v'^2 = 6.67x10^-11x5.972x10^24 / 6671000

Then v' = 7727.3 m/s