University of Rochester
Department of Physics and Astronomy
Physics123, Spring 2011
Homework 1 - SOLUTIONS
Conceptual Questions:
•
An astronaut orbiting around the earth wants to measure his weight. He has one
spring with constant k and a timer. Can he infer his weight on Earth? Explain.
Yes. The astronaut experiences an apparent weightlessness as in free fall (you can review
this concept in Giancoli 6-4). The astronaut can form a harmonic oscillator attaching her
body (of mass m) to the spring (of constant k). By minimizing possible damping forces,
her motion can be well described by a simple harmonic motion. Measuring with the timer
the period of oscillation, she has
2
m
⎛ T ⎞
T = 2π
→
m = k⎜ ⎟ .
⎝ 2π ⎠
k
The weight (on Earth) can then be calculated by multiplying m and the acceleration of
gravity at the Earth’s surface, g.
•
Is it possible to have damped oscillations when a system is at resonance? Explain.
Yes. (Without damping the amplitude would increase without limit at resonance.)
Problem 1.1 – Solution
(a)
The spring constant can be found from the mass and the frequency of oscillation.
(b)
The energy can be found from the maximum potential energy.
Problem 1.2 – Solution
Deuterium is the isotope of the element hydrogen with atoms having nuclei consisting of
one proton and one neutron.
k M D2
ω D2
fH
1
M D2 = 2M H 2 →
=
=
→ fD2 = 2 = 0.919 × 1014 Hz.
ω H2
k M H2
2
2
Problem 1.3 - Solution
Problem 1.4 - Solution