2 spheres, of unequal masses, hang on strings and are touching. Sphere a is pulled back to the left, string taught, and released, hitting sphere B at a known velocity. Sphere B's post impact velocity is known, and to the right.
i have to find A's post collision velocity.
Intuitively, I know it will be the difference between the impact velocity of A and the final velocity of B.
I can demonstrate this using conservation of momentum:
m1u1+m2u2 = m1v1 + m2v2
Should i do any other calculations?
No. As I read the question, u2 is zero.
Yes, it's zero. That seems to make the second term (m2u2) zero, but I still get what i think is the correct answer.
What should be my next approach?
(ma ua + mb ub)before = (ma va + mb vb)after
ua is known
ub is 0
so
ma ua = ma va + mb vb
but vb is known
so
ma va = ma ua - mb vb
so
va = (maua -mb vb)/ma
everything on the right is known
Thanks both, for the answers.
To find sphere A's post-collision velocity, you can solve for it using the conservation of momentum equation you mentioned:
m1u1 + m2u2 = m1v1 + m2v2
Where:
m1 = mass of sphere A
m2 = mass of sphere B
u1 = initial velocity of sphere A
u2 = initial velocity of sphere B
v1 = final velocity of sphere A
v2 = final velocity of sphere B
Since you already know the initial velocity of sphere A (u1), the initial velocity of sphere B (u2), the final velocity of sphere B (v2), and the masses of both spheres (m1 and m2), you can substitute these values in the equation.
However, you would need the final velocity of sphere A (v1) to solve for it. You can use the known information that the post-impact velocity of sphere B is to the right to determine the direction of v1.
If sphere B is moving to the right after the collision, then v2 will be positive. In this case, to find v1, you will subtract m2v2 from both sides of the momentum equation:
m1u1 + m2u2 - m2v2 = m1v1
Then, you can rearrange the equation to solve for v1:
v1 = (m1u1 + m2u2 - m2v2) / m1
Plug in the known values for m1, m2, u1, u2, and v2, and calculate v1 using this equation.
However, if sphere B is moving to the left after the collision, then v2 will be negative. In this case, to find v1, you will add m2v2 to both sides of the momentum equation:
m1u1 + m2u2 + m2v2 = m1v1
Again, rearrange the equation to solve for v1:
v1 = (m1u1 + m2u2 + m2v2) / m1
Plug in the known values for m1, m2, u1, u2, and v2, and calculate v1 using this equation.
So, depending on the direction of velocity v2, you will use either the subtraction or addition method to calculate v1.