A 1.50 kg object Is held 1.20 m above a relaxed, massless vertical spring with a
ID: 1607089 • Letter: A
Question
A 1.50 kg object Is held 1.20 m above a relaxed, massless vertical spring with a force constant of 300 N/m. The object Is dropped onto the (a) How far does the object compress the spring? Your response differs from the correct answer by more than 10%. Double check your calculations. m (b) How far does the object compress the spring if the same experiment Is performed on the moon, where g = 1.63 m/s^2? 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. to at least four-digit accuracy to minimize roundoff error. m (c) Repeat part (a), but now assume that a constant air-resistance force of 0.700 N acts on the object during its motion. Your response differs from the correct answer by more than 10%. Double check your calculations. mExplanation / Answer
inital gravitational potential energy Ei = m*g*(h+x)
after compressing to x
final elastic potential energy Ef = (1/2)*k*x^2
from energy conservation
Ef = Ei
(1/2)*k*x^2 = m*g*(h+x)
(1/2)*300*x^2 = 1.5*9.8*(1.2+x)
compression x = 0.395 m
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(1/2)*300*x^2 = 1.5*1.63*(1.2+x)
x = 0.148 m
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(c)
inital gravitational potential energy Ei = m*g*(h+x)
after compressing to x
final elastic potential energy Ef = (1/2)*k*x^2
from energy conservation
Ef = Ei - Wfricition
(1/2)*k*x^2 = m*g*(h+x) - F*x
(1/2)*300*x^2 = 1.5*9.8*(1.2+x) - (0.7*1.2)
x = 0.387 m
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