How Fast Do Two Identical Spheres Travel When They Meet in Space?

[Psyguy22]

Homework Statement

Two identical 28.5-kg spheres of radius 12.1 cm are 35.3 cm apart (center-to-center distance) and at rest in outer space. (You can assume that the only force acting on each mass is the gravitational force due to the other mass.)

a) If they are released from rest and allowed to fall toward one another, what is their speed when they first make contact?

Homework Equations

ΔE=ΔK+ΔU=0
K=.5mv^2
U=-Gm1m2/r

The Attempt at a Solution

Well ΔK would equal
[itex] M*v_i ^2-M*v_f ^2 [/itex] (because both are moving the 1/2's cancel out)
and ΔU is
[itex] -Gm_1 m_2 / r_i - (-Gm_1 m_2 / r_f) [/itex]

So solved for v I get
[itex] v= sqrt(-G m_2 / r_1 + G m_2 / r_2)[/itex]
which came out to be 6.131*10^-5 m/s which isn't right... I don't see where I went wrong/

 

[ehild]

Homework Statement

Two identical 28.5-kg spheres of radius 12.1 cm are 35.3 cm apart (center-to-center distance) and at rest in outer space. (You can assume that the only force acting on each mass is the gravitational force due to the other mass.)

a) If they are released from rest and allowed to fall toward one another, what is their speed when they first make contact?

Homework Equations

ΔE=ΔK+ΔU=0
K=.5mv^2
U=-Gm1m2/r

The Attempt at a Solution

Well ΔK would equal
[itex] M*v_i ^2-M*v_f ^2 [/itex] (because both are moving the 1/2's cancel out)
and ΔU is
[itex] -Gm_1 m_2 / r_i - (-Gm_1 m_2 / r_f) [/itex]

So solved for v I get
[itex] v= sqrt(-G m_2 / r_1 + G m_2 / r_2)[/itex]
which came out to be 6.131*10^-5 m/s which isn't right... I don't see where I went wrong/

I can not see either, if you do not show your work in detail. What have you used for r1 and r2?

ehild

 

[Psyguy22]

For r1 I have .121+.353+.121 which is .595 m
for r2, it's just .242 m

 

[lucasem_]

your value for r1 should just be .353 (like point masses) and you're correct that r2 is .242 (distance between centers of mass at collision). The spheres will not have much velocity, as gravity is a very weak force, so it shouldn't be surprising that the value is relatively small

 

[ehild]

For r1 I have .121+.353+.121 which is .595 m
for r2, it's just .242 m

The center-to center distance was given as 0.353 m , so r1=0.353.


ehild