A 1.4 kg object that stretches a spring 2.4 cm from its natural length when hang
ID: 1602470 • Letter: A
Question
A 1.4 kg object that stretches a spring 2.4 cm from its natural length when hanging at rest oscillates with an amplitude of 3.4 cm. The acceleration due to gravity is 9.81 m/s2.
a. Find the total energy of the system. Answer in units of J.
b. Find the gravitational potential energy at maximum downward displacement. Answer in units of J.
c. Find the potential energy in the spring at maximum downward displacement. Answer in units of J.
d. What is the maximum kinetic energy of the object? Answer in units of J.
Explanation / Answer
(A) when x = 2.4 cm = 0.024 m
m g = k x
1.4 x 9.8 = k (0.024)
k = 571.7 N / m
total energy = k A^2 /2
= (571.7) (0.034^2) /2
= 0.33 J
(B) PE = - 1.4 x 9.8 x (0.024 + 0.034)
= - 0.80 J
(C) Max spring PE = (571.7) (0.024 + 0.034)^2 /2
= 0.96 J
(D) Max KE = 0.33 J (from energy conservation)
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