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A 50kg mass attached to a 13m bungee is dropped from a bridge. Continued...?
If k = 180N/m how far below the bridge will the mass drop?
Okay, so I'm in a bit of a sticky situation here (i know basic physics, none of that ! )
So we have...
Epe (elastic potential energy) = -kx i do believe...
where K = 180, X = 13
Is that correct?
well if so...?
Epe = -180*13
then GPE = mgh, (energy conserved)
-2340 = 50*9.8*h
-2340 / 490 = h
4.77 = h
ISH DOES NOT UNDERSTAND???? 4.77m can't be the height of the bridge??
Best answer and 10 points for whomever can explain how to do this properly thanks ! (:
Basically, the distance below the bridge the mass drops will be equivalent to the length of the stretched bungee. The length of this bungee when in equilibrium is 13 metre. So, u need to find the displacement x using spring constant and gravitational force acting on the 50 kg mass and add it to this length.
Below is the solution using eculator(Find Distance from Acceleration, Mass, Spring constant in step 1 of the solve problem tool):
Using the expression(see reference):
F = ma
where:
m is the Mass = 50 kg
a is the Acceleration = -9.8 m s⁻²
we calculate the value for Force(F):
F = 50*(-9.8)
∴ F = -490.00000000000006
Using the expression(see reference):
x = ( - Fs)/k
where:
Fs is the Force = -490.00000000000006 N
k is the Spring constant = 180 kg s⁻²
we calculate the value for Displacement from equilibrium(x):
x = ( - (-490.00000000000006))/(180)
∴ x = 2.722 m
Adding this displacement to the length of the bungee, the mass will drop 13 + 2.722 = 15.722 metre.
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