Scaleward bound

Classical Mechanics Level 2

Shown above is a chihuahua riding a St. Bernard (both drawn to scale). The mass of the chihuahua and the St. Bernard are related by

m chihuahua = γ m St. Bernard m_\text{chihuahua} = \gamma m_\text{St. Bernard}

Approximately what is the value of γ \gamma ?

1/36 1/16 1/81 1/5

Josh Silverman by Josh Silverman

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Well, if we look at the two dogs, I would say the height of the St. Bernard is ∼ 3 \sim3 times that of the chihuahua. Also, he is about 4 times as long. Since the width of the heads are comparable with of the bodies, he is about 3 times as wide as the chihuahua as well. Writing this down, a rough volume comparison is

V St. Bernard ∼ ( 4 L chihuahua ) × ( 3 W chihuahua ) × ( 3 H chihuahua ) ∼ 36 V chihuahua V_\text{St. Bernard} \sim \left(4L_\text{chihuahua}\right)\times\left(3W_\text{chihuahua}\right)\times\left(3H_\text{chihuahua}\right)\sim 36 V_\text{chihuahua}

Therefore, the St. Bernard has about 36 times the volume that the chihuahua does. Assuming that dog density is the same across species, he would be about 36 times as massive as well.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice solution!

Snehal Shekatkar - 6 years, 11 months ago

I am impressed

Ezekiel Domini Quintal - 6 years, 11 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...