A stuntman lands safely in an air bag to break his fall form the top of a 6-story building. With reference to Newton's second law, explain how the air bag reduces the risk of injury to the stuntman.

Question

anonymous · Answer

Force = mass x acceleration. injury comes at high forces. so either the bag reduces your mass, or reduces your acceleration.

anonymous · Answer

and it certainly doesnt reduce your mass :)

shane_b · Answer

$$a=\frac{\Delta V}{\Delta t}$$$$F=ma=m\frac{\Delta V}{\Delta t}$$From the above it should be clear that increasing the amount of time over which a velocity is changing decreases the acceleration.  Decreased acceleration results in a decreased force.

Air bags reduce force by increasing the time interval which decreases the acceleration.

anonymous · Answer

what i think is that when its falling from the height , the  force of gravity is acting upon it thus producing acceleration relative to its mass. As it moves downward , the rate of change of velocity(acceleration) becomes high, thus storing high momentum inside means in order to retaliate or stop  its motion some opposite force has to be applied. That force in case of falling object is the air drag force. This force acts opposite to the gravity as to reduce the acceleration of falling object. To apply greater drag , greater area of the bag is to be exposed to it. so reducing the risk of damage can be easily understood through it.

anonymous · Answer

and secondly increasing the time of flight also reduces the acceleration of the falling object.

shane_b · Answer

He's landing on an air bag...not falling with one (like a parachute).  

The volume of air within the airbag and the rate of at which it deflates upon impact will determine the length of the impact time (where he goes from Vmax to 0m/s).  The longer the time interval is the "softer" the landing will be (less force as I mentioned in the first post).  Since he's only 6 stories up drag shouldn't even be a significant factor.  Assuming each story is 4m high, his fall time will be:$$t=\sqrt{\frac{2h}{g}}=\sqrt{\frac{(2)24m}{9.8m/s^2}}=2.21s$$That's not a lot of time for anything but gravity to affect his speed on impact.

anonymous · Answer

impulse = force  x  time = change in momentum. since change in momentum is constant ( from max at max velocity to zero) as the time require to change the momentum to zero is increase the force on body decreases.