Hurricane forces — Comparing the force from a 60 mph wind to a 120 mph wind

[Shaye]

Homework Statement:

The arrival of a hurricane is predicted with wind speeds of 120 mph (miles per hour). The force exerted by a 60 mph gale on the sides of a train locomotive has been measured and found to be F. Will the hurricane forces on the same locomotive be:

1. The same as F
2. Twice as large as F
3. Three times as large as F
4. Four times as large as F

Relevant Equations:

F=Δp/Δt and Δp = Δ(mv)

The marker wrote that the answer is 4 and it's because m and v double. I don't understand how m doubles??

 

[Orodruin]

Can you find an expression for m in terms of the air density and the wind speed?

 

[Shaye]

Can you find an expression for m in terms of the air density and the wind speed?

The only thing I can think of is p=m/v and m=pv and ke = 1/2(pv)*v^2...but I'm still at a loss

 

[Orodruin]

The only thing I can think of is p=m/v and m=pv and ke = 1/2(pv)*v^2...but I'm still at a loss

So, you now have impulse = mv and $m = \rho v A$ ... (you need the area to make a mass/time out of the density.

 

[haruspex]

The only thing I can think of is p=m/v and m=pv and ke = 1/2(pv)*v^2...but I'm still at a loss

That confused me. p is usually used for momentum and lowercase v for velocity, leading to equations like p=mv. So I think you mean $m=\rho V$, V being volume. But then you have $ke = 1/2(pv)*v^2$, which uses v for velocity and volume, so write $KE = 1/2(\rho V)*v^2$.
Next is to consider what volume of air impinges upon the train in time t.

 

[Orodruin]

That confused me. p is usually used for momentum and lowercase v for velocity, leading to equations like p=mv. So I think you mean $m=\rho V$, V being volume. But then you have $ke = 1/2(pv)*v^2$, which uses v for velocity and volume, so write $KE = 1/2(\rho V)*v^2$.
Next is to consider what volume of air impinges upon the train in time t.

Oh yes, using v instead of V for volume clearly confused me too to see what I expected to see. @Shaye Never use the same letter for different quantities in the same problem.

 

[Shaye]

Thanks @Orodruin and @haruspex. After much hand holding I eventually got it now lol