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First Posted: Jan. 31, 2018, 5:07 p.m. CST

Last Updated: Jan. 2, 2019, 1:32 a.m. CST

Last Updated: Jan. 2, 2019, 1:32 a.m. CST

PROBLEM

A person jumps from a fourth-story window 15.0m above a firefighter's safety net. The survivor stretches the net 1.0m before coming to rest. a) What was the average deceleration experienced by the survivor when she was slowed down to rest by the net? b) What would you do to make it 'safer' to generate a smaller deceleration: would you stiffen or loosen the net? Explain.

SOLUTION

Hint

What happened? Break the problem down into stages. What are the 3 main stages of this little physics "movie"? Think about it in terms of energy and work. There is gravitational potential energy, kinetic energy, the potential energy of a spring (if the net can be modeled as a spring), and the work done by the net on the girl.

(a)

Answer

Stage 1: person jumps off building and starts to free fall. So her initial downward velocity is zero but work is starting to be done by gravity in the downward direction.

Stage 2: the person makes contact with the firefighter's net. At this point, she has a certain amount of Kinetic Energy due to the speed she has built up between the time she jumped off the building and the time she made contact with the firefighter's net that will save her life. All 15.0m of gravitational potential energy has been transferred to her kinetic energy, and she has a certain amount of momentum. Be careful, though. She still has 1.0m of gravitational potential energy left to be accounted for, since she is still 1.0m above the bottom of the net. Gravity is still doing work on her. But what is also doing work on her is the net itself, between the time she makes contact with the net, and the time she stops at the bottom of the net.

Stage 3: the net brings her to a complete stop. This is at the bottom of the net. She has traveled a total of 16.0m at this point in time. Her velocity at this time is 0.

After this, she may bounce back up due to the potential energy stored in the net, but we do not need to consider this stage, since Stage 1, Stage 2, and Stage 3 gives us a sufficient number of equations.

Hint

Only looking at Stage 1 and Stage 3, what are the energy equations that we can write to solve this problem? What are we looking for? Do our equations have this variable in them?

Answer

Stages 1-3: The total amount of work that gravity does between the time she starts to free fall, and the time she stops at the bottom of the net, is mgh where h is 16.0m.

Stages 2 and 3: The total amount of work that the net does on the girl is W=Fd=mad where d=1.0m. a is the acceleration (deceleration, to be precise), and this is the variable we are looking for!

Hint

Put these equations together and get an equation with which we can solve for acceleration after contact with the net. Solve for a, cancel terms if necessary, since this saves us time, and THEN plug in the numbers. Be sure to use consistent units. It's easier to use standard units most of the time since there's less to keep track of.

Answer

Putting these equations together, we get mgh=mad. Remember, it's easier to work with the algebra if you do lazy evaluation and wait until the variable is solved for BEFORE plugging in the numbers, since numbers are units are bigger than greek variables or otherwise. Canceling terms and solving for a, we get a=gh/d=156.8m/s^2.

(b)

What would you do to make it 'safer' to generate a smaller deceleration: would you stiffen or loosen the net? Explain.

Hint

Since the work done by the net is F*d, we want to look for the term that makes the firefighter's net "safer." What term should be decrease to make things "safe".

Answer

It's just like hitting in football. A hard hit is when there is a large force or large acceleration over a smaller amount of time. This is just like pressure. Force over a larger area is a smaller pressure. So it really boils down to time.

Hint

Do we want a larger amount of time or a smaller amount of time to do the same amount of work?

Answer

Force equals change in momentum over change in time, just like a linebacker hitting a wide receiver. So if we increase the total amount of time to do this work, which is in the denominator, then the Force, which is in the numerator of the left hand side of the equation, DECREASES.

So, if we loosen the net, it would take longer to do the same amount of work on the person, which would decrease the force and thus also the acceleration on average, making it safer. Not that jumping out of windows into firefighter nets is safe or anything.

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This article was written by Anna Condor.
Anna is a personal trainer and fitness coach. She works out 6 days a week and has a biweekly blog that you can follow. Anna is currently working on a book, and is in the process of establishing a foundation to help individuals and families in developing countries without food or shelter.
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