Physics 281: Homework #3: due April 25
By the end of the week, there will be five problems (two from each lecture, plus a bonus).
- Estimate the thermal time constant for a potato. If placed in an oven,
where radiation and convection couple thermal energy to the skin, is the
aforementioned external coupling the chief bottleneck to energy transfer,
or is it conduction into the core?
- Imagine yourself naked in a variety of thermal scenarios. In order to
feel perfectly comfortable long-term, you must not lose heat faster than
your metabolism replaces the heat. Ignore the effects of body hair, or
physiological mechanisms to reduce heat loss. We're talking perfect comfort
here, not simply survival.
- Inside a room, what is the coldest the air/walls can be for you to
maintain comfort?
- Standing outside on a clear night (radiating to cold sky at effective
255 K), how warm must the air be for you to maintain comfort?
- Sitting in a tub of water, how cold can the water be for you to
maintain comfort?
- You would not be able to maintain comfort in outer space (no sight-line
to sun). How long would it take for you to freeze solid? Don't let this
happen to you!
- Estimate the number of pieces a dinner plate will break into if dropped
onto a hard floor. Assume some fraction of the energy goes into breaking
bonds. Besides assumptions about plate geometry, density, etc., you will
need a crude estimate of bond strength and unit cell spacing.
- You want to stand on a 2×4 beam (actually
measures 1.5 by 3.5 inches!) without breaking it and falling to your death.
We have four options constructed by combining the following two conditions
in all possible ways: cross-section is in tall or short (flat) orientation;
beam is firmly supported (zero slope) at one end (cantilever) and you stand
at the end or the beam is supported on two simple supports at both
ends (slope unconstrained), with you standing in the middle. How long can
the beam be in order to support your weight, if it would crack and fail
when the maximum strain (at place of greatest curvature and distance from
neutral surface) reaches 0.01? The maximum moments for the two beams
are FL and FL/4, where F is the force and
L is the total length.
- Invent a problem of your own in the spirit of this week's class topics.
You do not need to provide a complete solution, though you might outline
how it may go. The art is to strike a balance between trivial and hopelessly
complex.