Download Estimation Activity 3 Solutions

AP50 Fall 2014
Estimation Activity 3 Solutions
Th Oct 9
1) Estimate the chemical energy converted to kinetic energy during the explosive separation of a professional
fireworks shell. Answer units: [J]
Getting started
Think of the exploding shell as converting stored chemical energy to kinetic energy. Assuming that all pieces of the
shell fly apart at the same speed, we can calculate the energy released.
Devise plan
Execute plan
Estimate for m: 5kg
Estimate for v:
Assumption: Fireworks explode at approximately 100m height
Assumption: The radius of the explosion is approximately 1/10 the height (10m)
Assumption: The time for an ignited particle to reach its maximum radius is about 0.5s.
E = 103 J
order of magnitude = 3
Evaluate plan
Some fireworks are carbon based, meaning they are composed of gunpowder and charcoal. We can check the
reasonability of our answer by comparing it to the chemical energy converted to kinetic energy for a shell leaving
the muzzle of a gun, since this reaction is also relies on chemical reactions involving gunpowder. We can estimate
the mass of the shell as 200g and the muzzle velocity as 100 m/s. The kinetic energy of the shell at the muzzle is
then K=(1/2)mv2=(1/2)(0.2kg)(100 m/s)2=103 J, which is the same kinetic energy we estimated for a firework
explosion.
2) Estimate the relative speed of the moon as seen from an observer on the earth. Answer units: [m/s]
Getting started
We know that the earth rotates while the moon orbits, and that the difference between these two rates will give
us relative velocity. We can therefore subtract the velocity of the moon from the velocity of an observer on earth’s
surface. Linear velocities can be estimated using arc length formula.
Devise plan
AP50 Fall 2014
Execute plan
Assumption: Radius of earth = 6000km
Assumption: Radius of moon orbit = 380,000km
Assumption: Moon travels around earth in about 30 days
Assumption: 1 earth rotation is 24 hours
Vme = -9.2 * 102 m/s
order of magnitude: 3
Evaluate plan
To quickly estimate how reasonable this result is, we can consider that it takes the moon 30 days to complete an
orbit that is about 100 times larger than the rotation completed by the Earth in a day. Thus we can compare the
100𝑥
𝑥
70𝑥
velocity of each as
versus , we can simply calculate that the difference is approximately
or a bit more than
30
1
30
twice the original distance – 14000km traveled in a day. 14000 km per day translates to approximately 200 m/s
which is on the same order of magnitude as our calculated result. Alternatively, we can consider that the moon
has to travel a distance 100 times larger than the Earth within a given period, which translates directly to the
relative difference in velocity.
3) Estimate the power output by an average person completing a “stadium workout” where they run up and
down each section of the Harvard Stadium as fast as they can. Answer units: [W]
Getting started
Since the workout requires running up stadium sections, we can estimate the height climbed over the course of
the entire workout. Given a person’s weight, potential energy gain can be calculated. Estimating the time it would
take to complete the stadium run would provide all information necessary to estimate work.
Devise plan
AP50 Fall 2014
Execute plan
Assumption: m =70kg
Assumption: h = 600m. There are about 40 sections measuring about 15m high each, which multiplies to a total of
600m climbed.
Assumption: t =30 minutes
𝑃 ≈ 1.3 ∗ 102 𝑊
order of magnitude = 2
Evaluate plan
The same as a light bulb! This is reasonable because we know that some bikes have generator lights, and its
possible for a person to power the lights by pedaling.
4) Estimate the force exerted by the atmosphere on the entire surface of one person’s skin. Answer units: [N]
Getting started
Pressure = force/area, and we know atmospheric pressure is approximately 100,000Pa. We just need to estimate
the surface area of one human’s skin.
Devise plan
Execute plan
Assume A = 1-9 m2
𝐹 = 105 𝑁
order of magnitude = 5
Evaluate plan
We can find that an average adult has a skin surface area of 2 square meters, which is very close to the assumed
area. The calculated force given known atmospheric pressure is fairly straightforward and the large force is
reasonable when considering the force exerted by all of the molecules surrounding the skin in the atmosphere.
5) Estimate the height of the mountain a college student could climb with the energy saved by turning out their
dorm lights instead of keeping the lights on for an all-nighter homework assignment. Answer units: [m]
Getting started
Estimate the energy required to run a light bulb overnight, and then convert to potential energy to determine
height climbed.
Devise plan
AP50 Fall 2014
Execute plan
Assumption: Light bulb burns for 12 hours
Assumption: Light bulb is 100W
Assumption: Person is 70kg
ℎ = 6.3 ∗ 103 𝑚
order of magnitude = 4
Evaluate plan
We consider that a light bulb uses a significant amount of electrical power if used over the course of an entire
night. The calculation for the bulb usage in a single night is fairly straightforward given the translation between
watts and joules. To calculate the height a college student could climb using this energy, we consider only the
corresponding potential energy (for simplicity) and neglect other energy that might be needed to climb a height
almost equivalent to Mount Everest.