. The 2 kg block is given an initial velocity of 20m/s over the smooth rod (i. e. no friction is considered), when it is at A. If the spring has an unstretched length of 1 m and a stiff ness of k = 100 N/m, using conservation of energy determine the velocity of the block, when. s:3 m. g=9.81 nls2

Explanation:

Given:

Now the change in length of the spring under the weight of the block:

Now the kinetic energy of the block when the spring is unstretched:

Now the spring potential energy of the spring when it is compressed:

Now the remaining part  of the kinetic energy initially possessed by the body is the instantaneous kinetic energy of the block:

where:

change in energy

final kinetic energy at the given instant

Explanation:

mass of block, m = 2 kg

initial velocity, u = 20 m/s

spring constant, K = 100 N/m

elongation, Δx = 3 - 1 = 2 m

Let v be the velocity when s = 3 m.  

Use conservation of energy

100 x 2 x 2 = 2 x (v² - 400)

200 = v² - 400

v² = 600

v = 24.5 m/s