Answer to Question #257699 in Classical Mechanics for Matt

Question

Hello, I am trying to figure out the speed of wind it would take to move a bulk cart at the airport. The bulk cart was hit by jet blast and pushed into an aircraft. What was the wind speed from that jet blast?

The bulk cart is a rectangular metal box on wheels. The surface area hit by the blast is 1.5m x 1.5m. The cart weight 771.107kg. The cart moved 4.572m in 2.5 seconds before it struck the aircraft.

Can anyone help?

Answer 1

Hello. Without taking much aerodynamics into consideration, we can estimate the wind speed in the following way. First, find acceleration:

$$a=2d/t^2.$$

Determine the force created by the wind:

$$F=ma=2md/t^2.$$

On the other hand, force is pressure times surface area:

$$F=Ap=A\rho v^2.$$

Equate:

$$2md/t^2=A\rho v^2,\\\space\\ v=\sqrt{\frac{2md}{A\rho t^2}}=20.2\text{ m/s}.$$

The density of air is 1.229 kg/m³ in this calculation.