What is the speed of an alpha particle emitted from an atomic nucleus?

[psycovic23]

"An atomic nucleus initially moving at 420 m/s emits an alpha particle in the direction of its velocity, and the new nucleus slows to 350 m/s. If the alpha particle has a mass of 4.0u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?"

I did $$222u * 420 m/s + 0 = 222u * 350m/s + 4 u * X m/s$$ and I get 3885 m/s, but the answer says it's 4200. What did I do wrong?

 

[assyrian_77]

The mistake is in the RHS of your equation. The new nucleus does not have mass 222 u anymore, its new mass is 218 u.

 

[psycovic23]

Ah, I see. Thanks!

 

[psycovic23]

Here's another one...

A 1.0x10^3 kg Toyota collides into the rear end of a 2.2x10^3 kg Cadillac stopped at a red light. THe bumpers lock, the brakes are locked, and the cars skid forward 2.8m before stopping. The coefficient of kinetic friction between the tires are .40. What's the speed of the Toyota at impact?

I know that the equation is
$$1.0 * 10^3 v_1 = (1.0x10^3 + 2.2 * 10^3) v'$$

and that the force lost to friction is
$$3.2*10^3 kg * g * .40 = 35,123N$$

but I don't know how to find the v` of the equation...as I don't know where to get a second equation.
$$v_1 - v_2 = v_2' - v_1'$$
doesn't work since it just ends up equaling 0...how do I do this?

 

[Sirus]

$$\vec{F}_{friction}=m_{total}\vec{a}$$
Any equations of motion you can use that include displacement, acceleration, and velocities?

 

[psycovic23]

Ah...I get it! Tricky Thank you!