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:

kx_{1}^{2}/2 = kx_{2}^{2}/2+ mv^{2}/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/s^{2};

so

m = k(x_{1}^{2}-x_{2}^{2})/v^{2} = 9.6 (14.8^{2} - 7.4^{2})/32.7^{2} = 1.47 kg.

kx

where

k = 9.6 N/m, x1 = 14.8 x 10

so

m = k(x

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