Question

An Unstretched spring with a spring constant of 19.6 N/m is attached to a 2.6 kg block at rest on a horizontal table. A constant 23.6 N force is applied to stretch the spring 41 cm from its resting position. After being let go, what is the speed of the block as it passes equilibrium?

A. 3.4 m/s

B. 3.1 m/s

C. 2.5 m/s

D. 7.8 m/s

Answer 1

here,

the spring constant , K = 19.6 N/m

mass of block , m = 2.6 kg

x = 41 cm = 0.41 m

let the extension in the spring be A

K * A = F

19.6 * A = 23.6

A = 1.204 m

let the speed of the block as it passes through equilibrium be v

using conservation of energy

0.5 * K * A^2 = 0.5 * m * v^2

19.6 * 1.204^2 = 2.6 * v^2

solving for v

v = 3.4 m/s

the speed as it passes through the equilibrium is A) 3.4 m/s