Acceleration Equations for Unknown Masses

[dance_sg]

Homework Statement

13. Which expression represents an equality between accelerations?

A) Gm_e/r = v/r
b) Gm_e/r²= v/r
C) Gm_e/r²= v²/r
D) √Gm_e/r= v/r²

The Attempt at a Solution

i have no idea how to figure this out.

 

[rock.freak667]

If you can't automatically see it. Write out the units of each one and see if you get m/s² on the left and right sides.

Also, seeing the terms on the left side, do know a formula for acceleration? Do the same for the right side with the terms v and r.

 

[tms]

It's a question of units. In which answer, if any, do the left- and right-hand sides both have the units of acceleration?

 

[dance_sg]

so i know for sure answers b and c do, but what about the other sides. a=v/t is an equation, but that's not an option..

 

[tms]

so i know for sure answers b and c do, but what about the other sides. a=v/t is an equation, but that's not an option..

Since answers b and c are different in the right-hand side, they can't both be correct. It is a question of units, not of any particular equation that might represent an acceleration.

 

[dance_sg]

but for v and r, it would be m²/s, rather than m/s²

 

[tms]

v is m/sec, and r is m, so, for instance, v/r is
$$\frac{\text{m/sec}}{\text{m}} = \frac{1}{\text{sec}}.$$
Is that acceleration? You have to do the same kind of "calculation" for each possible answer.

 

[dance_sg]

o thank you! that makes way more sense. :D

 

[dance_sg]

i have one more question if u think you could answer it,
-When the distance separating two masses, M and m, is 1.2 x 1010 m, the gravitational force of attraction is 5.0 N. If the mass of M becomes 3M and the separation distance becomes
2.4 x 1010 m, what will be the force?

A. 0.27 N
B. 2.2 N
C. 3.8 N
D. 7.5 N

what equation am i suppossed to use for that??

 

[rock.freak667]

i have one more question if u think you could answer it,
-When the distance separating two masses, M and m, is 1.2 x 1010 m, the gravitational force of attraction is 5.0 N. If the mass of M becomes 3M and the separation distance becomes
2.4 x 1010 m, what will be the force?

A. 0.27 N
B. 2.2 N
C. 3.8 N
D. 7.5 N

what equation am i suppossed to use for that??

gravitational force of attraction

Maybe a formula that contains M,m and an r ? Perhaps a constant like G in it as well.

 

[tms]

You're supposed to use the equation for for the gravitational force between two bodies.

You should also start a new thread for a new question, so other people can find it easily.

 

[dance_sg]

but taht formula doesn't have force in it.

 

[tms]

Sure it does; it defines the force.

 

[dance_sg]

o sorry. i will know for next time. and ok. so Fg=GmM/r^2. but in the equation it tells us the distance between the two. not what each equals. how do i solve that?

 

[tms]

You can write two equations: one for the initial conditions, and one for the second set of conditions. G is known; you are given the force in the first situation, and the distances; you are given the second set of masses in terms of the first; but you don't know the masses m and M. You need to somehow get rid of m and M from the equations. If you actually write down the equations, the technique should jump out at you.