Calculating Mass and Velocity in Elastic Collisions: Lab Cart A and B Example

[runningirl]

Homework Statement

Lab cart A(v=1.5 m/s; m=.25 kg) collides elastically with lab cart B (v=0m/s; m=?). After the collision, the velocity of cart A is -.67 m/s. Cart B then goes on to have a sticky collision with cart C (v=0 m/s; m=.50 kg). After the sticky collision, the velocity of the combined carts B and C is 0.47 m/s. What is the mass of cart B? What as the velocity of cart B right after cart A collided with it?




3. The Attempt at a Solution

m1v1+m2v2=m1vf1+m2vf2

.25(1.5)+m(0)=.25(-.67)+m(vf2)

mv1+.5(0)=(m+.5)(.47)

i wanted to substitute m or v to solve for them each...

i got m=.65 kg and v=.83 m/s.

but i wasn't sure if my method was correct.

 

[issacnewton]

Lab cart A(v=1.5 m/s; m=.25 kg) collides elastically with lab cart B (v=0m/s; m=?). After the collision, the velocity of cart A is -.67 m/s. Cart B then goes on to have a sticky collision with cart C (v=0 m/s; m=.50 kg). After the sticky collision, the velocity of the combined carts B and C is 0.47 m/s. What is the mass of cart B? What as the velocity of cart B right after cart A collided with it?

m1v1+m2v2=m1vf1+m2vf2

.25(1.5)+m(0)=.25(-.67)+m(vf2)

mv1+.5(0)=(m+.5)(.47)

i wanted to substitute m or v to solve for them each...

i got m=.65 kg and v=.83 m/s.
.

you see, the velocity of the cart B after it collides with cart A (vf2) is same as the velocity of the cart B before it collides with cart C (v1) which I have highlighted above. Since you have already used the symbol v1 as the velocity of the cart A before it collides with the cart B, don't use it again for the velocity of the cart B before it collides
with cart C.

 

[runningirl]

thanks. but is my method correct?

 

[issacnewton]

yes, so you have now two equations and two unknowns, mass of cart B (m) and the velocity of the cart B after the collision with cart A and before the collision with cart C (vf1). so solve for these.