Sarita,
The jumper's Kinetic energy 1/2m v2=mgh where h=42' and m=150/32.2 slugs at this point you have a moving mass starting to stretch a spring (assume linear) so the kinetic energy will be transferred to potential energy by stretching the spring so we have mgh=1/2kx2 where k is the spring constant (16 lb/ft) and all you have to do is solve for x which is how much the spring had to stretch to absorb the energy of the falling mass. This all assumes that 42+x < the distance from the ledge to the ground :-)
Hop this helps
Jim
Jim S.
tutor
solving for x gives x=(2mgh/k)^.5=(2*150*42/16)^.5=28.1 ft is the amount the bungee is stretched.
Not sure what you were trying to do above. The spring potential energy is (1/2)*k*x2 not 1/(2*k*x2).
Let me know if you don't get it.
Jim
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08/28/15
Sarita C.
Ok, I need to solve the inequality for S. My professor stated no equal signs allowed. She also stated I will have two positive critical values, and one negative critical value that I can ignore because their is negative stretch.
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08/31/15
Jim S.
tutor
Ah yes I see....first of all I assume that you have had basic algebra??? an equation of the form x2=k where k is any real number >0 has a solution x=±(k)1/2 these kind of equations arise in physics often and you have to choose the physically appropriate solution. In the is problem we know that the bungee will elongate we therefore choose the positive solution.
I reread the problem and the stiffness of the cord is no less than 16 lb/ft so that means k≥16 lb/ft so that means that S<(2mgh/k)^.5... the stiffer the cord the less it will stretch, make sense?
Jim
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08/31/15
Sarita C.
08/28/15