Funny Pics II: The Revenge

[L. Marcus]

A zoomed-out picture of Valles Marineris ...

[Pariah]

14 minutes ago, Logan.1179 said:

 

A falling coyote (m=20 kg) leaves a crater 10 cm deep in the desert floor upon impact. If the density of packed desert sand is 1682 kg/m³, calculate:

• a. The force exerted by the coyote on the ground upon impact;
• b. The force exerted by the ground on the coyote;
• c. How fast the coyote was falling; and
• d. How far above the ground was the coyote when he realized he was running in the air? (Assume no loss of energy due to air resistance.)

Show all calculations for full credit.

 

[Logan D. Hurricanes]

That's more than 10 cm!

[L. Marcus]

Coyotes are smaller than you think. Can we assume a coyotal density of about 1 kg/dm^3?

[Pariah]

I think most mammals are around 1000 g/L, so that's probably fine.

[Logan D. Hurricanes]

 As if Wile E Coyote was "most mammals".

 

 

[L. Marcus]

I've never seen him mam.

[Ternaugh]

2 minutes ago, L. Marcus said:

I've never seen him mam.

 

[Starlord]

He cleans up pretty good, but he's no Bugs Bunny

[Cancer]

1 hour ago, Pariah said:

 

A falling coyote (m=20 kg) leaves a crater 10 cm deep in the desert floor upon impact. If the density of packed desert sand is 1682 kg/m³, calculate:

• a. The force exerted by the coyote on the ground upon impact;
• b. The force exerted by the ground on the coyote;
• c. How fast the coyote was falling; and
• d. How far above the ground was the coyote when he realized he was running in the air? (Assume no loss of energy due to air resistance.)

Show all calculations for full credit.

 

 

Initial comments:  Three possible cases to compute here.  First case is a subsonic impact, where the impact velocity is below the sound speed in the target surface, and the elasticity of the material in the surface material provides the means to launch surface material vertically upward.  Second case is a hypersonic impact, where the impact velocity is several times the sound speed in the target material, and the vaporization and subsequent explosion of the impactor below the original surface excavates the crater.  (In general hypersonic impacts ought to make only craters of circular shape, but we ignore that detail here.)  Third case is impact at approximately sound speed, and that acoustic modes are excited that launch some substrate material upward.  (This process has the capacity to make complex shapes for the excavated cavity, but those depend also upon material that lies under the surface layer, and rather than make speculative computations we will skip this case.)

 

Hypersonic impact is easiest.  Shoemaker (1983 Ann. Rev. Earth Planet. Sci., vol 11, p. 461) gives

and plugging in appropriate values for crater diameter, crater collapse factor, alluvium and target material densities, that gives a value for W, the kiloton TNT equivalent yield for the kinetic energy at impact of the infalling object, which can be related to the bolide's diameter, density, and velocity.  Pushing estimates around for a 20-kg falling mass suggests an impact velocity in the neighborhood of (c) 10 km/s, for a total momentum of 2e+5 kg m/s.  That gets brought to zero in about 1e^-5 seconds, and using F ~= delta p/delta t, this means (a) the force at impact averages about ten billion newtons.  (b) By Newton's 3rd Law, the force of ground upon coyote is equal in magnitude and opposite in direction.  For realization time (d), we note that nerve signal propagation speed is very roughly 120 m/s, and timing the source material suggests about 0.5 s for the reaction time.  On the other hand, to reach a falling velocity of 10 km/s in a 1-g gravity field takes about 1000 seconds, and the reaction time is rather less than this, so this suggests the coyote was aware of the impending impact for about 15 minutes.  Clearly, some of the falling time has been edited out of the source videos for the sake of brevity.

[Old Man]

1 hour ago, Cancer said:

 

Initial comments:  Three possible cases to compute here.  First case is a subsonic impact, where the impact velocity is below the sound speed in the target surface, and the elasticity of the material in the surface material provides the means to launch surface material vertically upward.  Second case is a hypersonic impact, where the impact velocity is several times the sound speed in the target material, and the vaporization and subsequent explosion of the impactor below the original surface excavates the crater.  (In general hypersonic impacts ought to make only craters of circular shape, but we ignore that detail here.)  Third case is impact at approximately sound speed, and that acoustic modes are excited that launch some substrate material upward.  (This process has the capacity to make complex shapes for the excavated cavity, but those depend also upon material that lies under the surface layer, and rather than make speculative computations we will skip this case.)

 

Hypersonic impact is easiest.  Shoemaker (1983 Ann. Rev. Earth Planet. Sci., vol 11, p. 461) gives

and plugging in appropriate values for crater diameter, crater collapse factor, alluvium and target material densities, that gives a value for W, the kiloton TNT equivalent yield for the kinetic energy at impact of the infalling object, which can be related to the bolide's diameter, density, and velocity.  Pushing estimates around for a 20-kg falling mass suggests an impact velocity in the neighborhood of (c) 10 km/s, for a total momentum of 2e+5 kg m/s.  That gets brought to zero in about 1e^-5 seconds, and using F ~= delta p/delta t, this means (a) the force at impact averages about ten billion newtons.  (b) By Newton's 3rd Law, the force of ground upon coyote is equal in magnitude and opposite in direction.  For realization time (d), we note that nerve signal propagation speed is very roughly 120 m/s, and timing the source material suggests about 0.5 s for the reaction time.  On the other hand, to reach a falling velocity of 10 km/s in a 1-g gravity field takes about 1000 seconds, and the reaction time is rather less than this, so this suggests the coyote was aware of the impending impact for about 15 minutes.  Clearly, some of the falling time has been edited out of the source videos for the sake of brevity.

 

Are we even accounting for atmospheric drag in this calculation?  The problem as stated does not direct us to neglect the effect of air resistance, and rather implies the opposite in part d.

[Pariah]

* munches popcorn *

[Cygnia]

[Certified]

2 hours ago, Cygnia said:

 

[Cancer]

If the coyote's impact crater is in the subarctic, and fills with water, you'll get a lake to which you can give a name like "Elgygytgyn".

[Logan D. Hurricanes]

[Logan D. Hurricanes]

[Cygnia]

[Cygnia]

[Logan D. Hurricanes]

 

That's about 1/4 a giraffe. 

[Clonus]

[Logan D. Hurricanes]

Apparently, pop stars are the new unit of measurement. 

 

[dmjalund]

2 hours ago, Logan.1179 said:

 

That's about 1/4 a giraffe. 

Americans will use any measurement to avoid using the metric system

[Cygnia]

[Cancer]

There seems to be pushback about using the firkin.  Nine US gallons.  Too big to be growler.