Question

Cart A of inertia m has attached to its front end a device that explodes when it hits anything, releasing a quantity of energy E. This cart is moving to the right with speed v when it collides head-on with cart B of inertia 2m traveling to the left at the same speed v. The explosive goes off when the carts hit, causing them to rebound from each other. The initial direction of motion of cart A (to the right) is the +x direction.

If one-quarter of the explosive energy is dissipated into the incoherent energy of noise and deformation of the carts, what is the final velocity of cart A? in E,v,m

Answer 1

Hey!

Answer 2

Hello! I am sorry, I know that this is not a mathematics question, but the reason why I can"t solve this is that I get 2 equations with two unknowns from momentum and energy equations, and I cannot leave v final alone...

Answer 3

Let \(v_a, v_b\) be the velcities after collision

Conservation of momentum :
\[mv+2m(-v) = mv_a + 2mv_b\tag{1}\]

Conservation of mechanical energy :
\[\frac{1}{2}mv^2 + \frac{1}{2}(2m)v^2+E = \frac{1}{2}m{v_a}^2 +\frac{1}{2}m{v_b}^2+\dfrac{1}{4}E\tag{2}\]

two equations and two unknowns : \(v_a, v_b\).
should be solveable, right ?

Answer 4

Yes I know, at first look that is what I told to myself. But when I left \[v _{a}\] alone in the first equation, and square to get \[v _{a}^{2}\] , I realized that I cannot factor out v of a ...

Answer 5

I realized I cannot factor out v of a in the energy equation*

Answer 6

v of a in the energy equation*