Newtonian - Force, Gravity, and Bungee Jumping

AI Thread Summary
The discussion revolves around calculating the force exerted by a bungee cord when a 55kg person jumps off a bridge, experiencing a downward acceleration of 7.8m/s². The net force is determined using the equation ΣF = ma, resulting in a calculated force of -418N when considering the downward acceleration. The force of gravity acting on the jumper is 539N, leading to the conclusion that the bungee cord must exert a force of +121N to reduce the descent to the specified acceleration. The reasoning for subtracting the forces is to determine the additional force required by the bungee cord to counteract gravity and achieve the desired acceleration. This analysis highlights the relationship between gravitational force and the force exerted by the bungee cord during the jump.
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Homework Statement


A person weighing 55kg jumps off of a bridge with a bungee cord attached. The problem seeks to find the bungee cords Force vector when the acceleration is 7.8m/s2 in the downward direction.

m = 55kg
a1 = g = 9.8m/s2

To find:
F1 when a2 = 7.8m/s2 downward.

I've specified my grid as \uparrow+ \rightarrow+ so the accelerations are technically negative.

Homework Equations


\SigmaF = ma


The Attempt at a Solution


\SigmaF = ma
\SigmaF=55kg(-7.8m/s2)
\SigmaF = -418N

\SigmaF = F1 - F2
\SigmaF = 539N - 418N
Force of bungee cord acting = +121N
 
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Why did you subtract the forces?
 
semc said:
Why did you subtract the forces?

The 539N was the Force with F=ma and a = g. I think I forgot to write that.
The -428N was the Force with F=ma and a = 7.8m/s2.

My inclination was to subtract the forces to get the force required by the bungee cord to slow the decent to the 7.8m/s2
 
Well since gravitational force is downwards and he is traveling downwards...
 

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