FORCE QUESTION...help:)?

Question

sara is a cosmonant engineer in the spacecraft vostok// orbiting the earth at an altitude of 520 km with a speef of 7.6km/s sara's mass is 65kg and the radius is 6.37*10^6 what is her acceleration? what gravitaional force does the earth exert on sara?

Answer 1

Well, we know there's no tangential acceleration.  Why?  Because she's going around in orbit with constant speed.  So how can she be accelerating?

The answer is that she has radial acceleration.  You can think of it as her "falling" constantly towards Earth.  Your book has an equation for radial acceleration which should look like this: F = ma = m(v^2/r)

Notice that you have all the variables you need to plug in: the mass of the woman, her speed (don't forget to change it to m/s), and the radius of the orbit (add the orbit height to the Earth's radius for that).  That'll help you get the force.

The acceleration, as you can see, is just the force divided by Sara's mass.

Remember this equation, because you'll need to have it memorized for future Physics courses if you take them.

Good luck!

Answer 2

Since she is going in a circle the force on her must equal the centripetal force corresponding to her radius.  therefore, the force on her is in the radial direction given by

(v^2)/r

This is also the gravitational acceleration at her radius

GM/r^2  where G is the universal gravitational constant and M is the mass of the earth.

The force on her is just her mass times the acceleration or

F = mv^2/r = GMm/r^2

Clearly the centripetal equation is easer to use in this problem