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Answer to Question #1357 in Mechanics | Relativity for Jon ALlen

Question #1357
A block of unknown mass is attached to a
spring of spring constant 9.6 N/m and undergoes simple harmonic motion with an amplitude of 14.8 cm. When the mass is halfway
between its equilibrium position and the end-point, its speed is measured to be 32.7 cm/s.
Calculate the mass of the block.
Answer in units of kg.
Expert's answer
We can use the law of enegry conservation:
kx12/2 = kx22/2+ mv2/2
where
k = 9.6 N/m, x1 = 14.8 x 10-2 m , x2 = 7.4 x 10-2 m, v = 32.7x10-2 m/s2;
so
m = k(x12-x22)/v2 = 9.6 (14.82 - 7.42)/32.72 = 1.47 kg.

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