You are investigating a newly discovered particle X that has an unknown mass M and moves with a constant but unknown speed u. In your experiments you observe collisions between particle Xand different test particles with known masses m that are initially at rest. You let the particles collide head-on and stick together, and you measure the speed v of the combined-particle object. From other observations you know that in all experiments the objects move along the same straight line before and after the collision. Your data are shown in the table. Note that the masses are expressed in units of reference mass m0 and the speed in units of reference speed v0.

Derive an expression for v.

v = Mu/(M+m)

We assume that no external impulses are exerted on the system of two particles, so the total momentum of the system is the same before and after the collision.

Determine u using the data in the table. (Hint: Rearrange the expression that you derived to obtain a new equation with the linear dependence on m.)

Express yourt answer in terms of v0.

u=

Determine M using the data in the table. (Hint: Rearrange the expression that you derived to obtain a new equation with the linear dependence on m.)

Express yourt answer in terms of m0.

M=

m(mo) v(vo) 0.55 0.45 0.35 0.30 0.25 2.0 4.0 6.0 8.0 10.0