Energy Problems - Springs You decide to take the plunge and go bungee jumping. B
ID: 3897628 • Letter: E
Question
Energy Problems - Springs You decide to take the plunge and go bungee jumping. Being a college student, you do this on the cheap, and buy a bungee cord with a spring constant of k = 500.0 N/m and a length of L = 8.0 in. You choose a bridge where you tie the end of the cord so you can jump off. Assume that you step oft the bridge with zero speed. How high must the bridge be so that you can do this fun jump more than once? (Being nervous, you want to be extra safe. How will air resistance affect your calculation?) A spring is attached to a ceiling, and has a relaxed length of 25.5 cm. When a mass of 0.80 kg is attached to the spring it stretches to an equilibrium length of 34.5 cm. Find the spring constant of the spring. I lift the mass until the spring returns to its relaxed length, and then release it. When the mass returns to the equilibrium length, what is its speed? After I release the mass and it falls, what is the length of the spring when the mass reaches its lowest point?Explanation / Answer
b)
as we have life mass upto it's relaxed length
amplitude = 0.345-0.255 = 0.09
now,
Total energy of spring = 1/2*k*A^2
Total energy of spring = KE at Equilibrium ....(as at equilibrium PE=0)
so,
1/2*m*v^2 = 1/2*k*A^2
v = sqrt(k*A^2/m) = sqrt(87.2*0.09^2/0.8) = 0.94 m/s
c)
lowet point = equilibrium length + Amplitude(A) = 0.345+0.09 = 0.435 m = 43.5 cm
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