Question

Consider two blocks on a horizontal plane where block one has a small mass (m) with some velocity (v) while block two has a large mass (M) and a spring with a spring constant of (k). Have block one collide with the spring of block two and stick so that the two blocks are allowed to oscillate. Ignore friction.

1) Find the internal energy change in the system

2) Now assume block two is instead an un-moving wall so that
when the first box collides it creates a simple harmonic
oscillator, find the kinetic and potential energy of the harmonic
oscillator if the system oscillates at an angular frequency equal
to (k/m)^{0.5}

3) Find the increase in temperature (delta T) in the system by finding the mean KE of the oscillator (using part 2 over one vibrational period T=(2*pi)/(angular frequency)) deviding the energy among the number of atoms in the first block and equating this mean kinetic energy to 1/2*(Boltzmann's constant)*(delta T). Use v=1 m/s and m=1 kg if needed.

Answer #1

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