Sample Problem Force And Motion 11
Igor is a cosmonaut-engineer on the International Space Station, in a circular orbit around Earth, at an altitude h of 520 km and with a constant speed v of 7.6 km/s. Igor’s mass m is 79 kg.
SOLUTION: The Key Idea here is that Igor is in uniform circular motion and thus has a centripetal acceleration of magnitude. The radius of Igor’s motion , where R£ is Earth’s radius .
This is the value of the free-fall acceleration at Igor’s altitude. If the were lifted to that altitude and released, instead of being put into orbit there, he would fall toward Earth’s center.
SOLUTION: There are two Key Ideas here. First, there must be a centripetal
force on Igor if he is to be in uniform circular motion. Second, that force is the gravitational force on him from Earth.
If Igor were to stand on a scale placed on the top of a tower with height h = 520 km, the scale would read 660 N.