As part of your daily workout, you lie on your back and push with your feet agai
ID: 1451925 • Letter: A
Question
As part of your daily workout, you lie on your back and push with your feet against a platform attached to two stiff springs arranged side by side so that they are parallel to each other. When you push the platform, you compress the springs. You do 79.0 J of work when you compress the springs 0.480 m from their uncompressed length.
(a) What magnitude of force must you apply to hold the platform in this position?
329.166 N
(b) How much additional work must you do to move the platform 0.480 m farther, and what maximum force must you apply?
J
N
Explanation / Answer
= 1/2kx² = 1/2k(0.48)²
79 = 1/2k(0.48)²
79 = 0.1152k
k = 79/0.1152 = 685.763 N/m
F = kx = (685.763)(0.48) = 329.166 N (ANS)
b)
Work against spring = 1/2kx² = 1/2( 685.763)(0.98)²
Work against spring = 330 J
compare with 0.2 m compression difference is:
330 - 79 = 250 joules (ANS)
Force = kx = (4000)(0.4) = 1600 N
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