This problem concerns a collection of N identical harmonic oscillators (perhaps an Einstein solid or the internal vibrations of
gas molecules) at temperature T. The allowed energies of each oscillator are 0, hf, 2hf, and so on. We will use the infinite series 1 + x + x 2 + x 3 + · · · = 1 1 − x , 0 < x < 1 (a) Evaluate the partition function for a single harmonic oscillator. (b) Find an expression for the average energy of a single oscillator at temperature T. (c) What is the total energy of the system of N oscillators at temperature T? (d) Compute the heat capacity C = dU dT , and find the limit of C at T → 0: prove that it satisfies the third law of thermodynamics
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Answer:
where L is the length of the ramp
Explanation:
Let L (m) be the length of the ramp, and g = 9.81 m/s2 be the gravitational acceleration acting downward. This g vector can be split into 2 components: parallel and perpendicular to the ramp.
The parallel component would have a magnitude of
We can use the following equation of motion to find out the final velocity of the book after sliding L m:
where v m/s is the final velocity, = 0m/s is the initial velocity when it starts from rest, a = 2.87 m/s2 is the acceleration, and
is the distance traveled:
Answer:
5.98 m
Explanation:
= 11.15*4.6²/(4π²) = 5.98 m