A 1.30-kg object is held 1.25 m above a relaxed, massless vertical spring with a

Question

A 1.30-kg object is held 1.25 m above a relaxed, massless vertical spring with a force constant of 315 N/m. The object is dropped onto the spring. How far does the object compress the spring? Repeat part (a), but this time assume a constant air-resistance force of 0.650 N acts on the object during its motion. Your response differs from the correct answer by more than 10%. Double check your calculations, m How far does the object compress the spring if the same experiment is performed on the Moon, where g = 1.63 m/s^2 and air resistance is neglected? Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error, m

Explanation / Answer

let h be distance through which the spring is compressed.

a)
Initial potential energy of the object is 1.3*9.8*(1.25+h)
This is equal to the potential energy of the compressed spring
1.3*9.8*(1.25+h) = 0.5*315*h²

157.5h2-15.925h-15.925 =0
Solving for h
h = 0.37m
--------------------------------------...
b)
1.3*9.8*(1.25+h) – 0.65*(1.25+h) = 0.5*315*h²
h = 0.35517m
---------------------------------
c
1.3*9.8*(1.25+h)/1.63 = 0.5*315*h²
1.3*9.8*(1.25+h) = 1.63*0.5*315*h²
h = 0.28200 m

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