Exercise 14.23 A small block is attached to an ideal spring and is moving in SHM

Question

Exercise 14.23

A small block is attached to an ideal spring and is moving in SHM on a horizontal, frictionless surface. The amplitude of the motion is 0.110 m . The maximum speed of the block is 3.77 m/s .

Part A

What is the maximum magnitude of the acceleration of the block?

Express your answer with the appropriate units.

Exercise 14.23

A small block is attached to an ideal spring and is moving in SHM on a horizontal, frictionless surface. The amplitude of the motion is 0.110 m . The maximum speed of the block is 3.77 m/s .

Part A

What is the maximum magnitude of the acceleration of the block?

Express your answer with the appropriate units.

Explanation / Answer

Amplitude .. r = 0.11 m .. .. the radius of the equivalent circular motion

Max. accel occurs at max displacement (x = r)

From .. a = (-) ² x .. (equation for shm)
a(max) = ² r ---------------- (A)

= v(max) /r .. (from equiv.circular motion) .. 3.77 m/s / 0.11m .. = 34.27 rad/s

Substituting = 34.27 into (A) ..

a(max) = (34.27)².(0.11m) .. .. .. a(max) =129.18 m/s²

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