Solve For Velocity A horizontal spring is lying on a frictionless surface. One e

Question

Solve For Velocity

A horizontal spring is lying on a frictionless surface. One end of the spring is attached to a wall, and the other end is connected to a movable object. The spring and object are compressed by 0.065 m, released from rest, and subsequently oscillate back and forth with an angular frequency of 11.3 rad/s. The work done by nonconservative forces is zero. (a) Write down the mathematical expressions of the initial and final mechanical energies of the system. (b) What is the speed of the object at the instant when the spring is stretched by 0.048 m relative to its unstrained length? Express your answer with 2 significant figures.

Explanation / Answer

angular frequency w^2 = (k/m)

11.3^2 = k/m

spring constant k = 127.7 m

x1 = 0.065 m , x2 = 0.048 m

from conservation of energy

E1 = E2

0.5kx1^2 = 0.5mv2^2 +0.5kx2^2

(127.7m)x1^2 = m*v2^2 + (127.7mx2^2)

127.7*0.065^2 = v2^2 + 127.7*0.048^2

v2 = 0.50 m/s

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