Yahoo Answers: Answers and Comments for Physics Question? [Physics]
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Mon, 09 Apr 2018 02:53:55 +0000
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Yahoo Answers: Answers and Comments for Physics Question? [Physics]
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https://answers.yahoo.com/question/index?qid=20180409025355AAjamN5
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From NCS: GPE becomes SPE
mgh = ½kh²
k = 2mg / h = 2*96*...
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Mon, 09 Apr 2018 21:08:49 +0000
GPE becomes SPE
mgh = ½kh²
k = 2mg / h = 2*96*9.81 / 192 = 9.81 N/m
period T = 2π√(m/k) = 2π√(96 / 9.81) = 19.655 s
so we can model the motion with
y = h/2 + (h/2)cos(2πt/T)
where h/2 = amplitude = 96 m
and 2π/T = 2π/19.665s = 0.320 rad/s
so
y = 96 + 96cos(0.320t) → for y in meters and t in seconds
Then v = dy/dt = 96 * 0.320 * sin(0.320t) = 30.7sin(0.320t)
for v in m/s.
At t = 3.8 s, we have
v = 30.7*sin(0.320*3.8) = 28.8 m/s
(that is, down)
KE = ½mv² = ½ * 96kg * (28.8m/s)² = 40 000 J = 40 kJ
to two significant digits (39 712 J before rounding).

From oubaas: 2*m*g*h = k*h^2
k = √2*96*g/192 = √g N/m
m*g...
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Mon, 09 Apr 2018 09:11:51 +0000
2*m*g*h = k*h^2
k = √2*96*g/192 = √g N/m
m*g*h = m*g*(hΔh)+m/2*2*Δh*g+(√g)*(Δh)^2/2
2*m*g*(192192+ΔhΔh) = √g*(Δh)^2
2*m*√g = (Δh)^2
Δh = √2*m*√g = √2*96*3.132 = 24.52 m
Ekx = m/2*V^2 = 46*2*g*Δh = 19.62*24.52*46/1000 = 22.130 kjoule

From Amy: The elastic potential energy at 192m extension...
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Mon, 09 Apr 2018 03:11:24 +0000
The elastic potential energy at 192m extension is equal to the gravitational potential energy at 192 m high.
1/2 k (192 m)^2 = (96 kg) (9.81 m/s^2) (192 m)
k = 9.81 kg/s^2
That means her acceleration is:
a = g  kx/m = 9.81  0.102 x m/s^2
where x is distance fallen in meters.
Solve the differential equation to relate distance to time.