momentum and collisions

Question

A block of mass m₁ = 17 kg slides along a horizontal surface (with friction, μ_k = 0.37) a distance d = 2.4 m before striking a second block of mass m₂ = 9.75 kg. The first block has an initial velocity of v = 9.75 m/s.

A) assuming that block one stops after it collides with block two, what is block twos velocity after impact in m/s?

b) how far does block 2 travel d2 in meters before coming to rest after the collision?

Answer 1

So Lauren A.,

It would help if you indicated how far you were able to analyse this problem yourself, rather than just throwing it up as a question, along with your hands?

So think about what went on. There was friction, thus block 1 was accelerating (slowing down). Write the equations for the frictional force and acceleration, then write the equation for initial velocity, final velocity (your unknown), distance, and acceleration of block 1. Solve for that final velocity (as it hits block 2). That gives you info for a momentum, also!

Next, since block 1 stopped, it MUST have imparted all of its momentum to block 2. Momentum must be conserved! So put all of that incoming momentum into block 2, and solve for its velocity after impact.

Next, block 2 slows down (assume the same kinetic friction constant). Solve for its initial velocity, final velocity, acceleration, and distance. (The distance is your unknown).

Note something odd -- what happened to the kinetic energy during the collision? If momentum is conserved, and kinetic energy is converted to heat, you would not expect a heavier object to stop on collision, would you? That would require an INPUT of kinetic energy.

Which is why someone is writing such problems, rather than having a more well-paying job as an engineer, perhaps? Just sayin'.

-- Cheers, --Mr. d.