A 5.00-kg block is moving at vo = 6.00 m/s along Agure P6.79 a frictionless, horizontal sur-face toward a spring with force constant k = 500 N/m that is attached to a wall (Fig. P6.79). The spring has negligible mass. (a) Find the maximum distance u0 = 6.00 m/s k = 500 N/m -4— WW1 . .00 kg the spring will be compressed. (b) If the spring is to compress by no more than 0.150 m, what should be the maximum value of up?

a) The maximum distance compressed by the spring = 0.6m

b) 1.5m/s

Explanation:

mass of the block m= 5.00kg

Initial velociy of the block (v₀) = 6.00m/s

spring constant of the block is (k) = 500N/m

a) The maximum compression in the spring can be calculated as

initial kinetic energy is given by

 -----------------(1)

Final kinetic energy of the block is given by

------------------(2)

Change in kinetic energy of the block

ΔKE =

       =

The work done by the spring is stored in the form of potential energy of the block

is the maximum compressed distance of the spring

The loss in the kinectic energy will be converted to the potential energy of the block

ΔKE =

The maximum distance compressed by the spring = 0.6m

b) The maximum compressed in the spring = 0.150m

let the initial velocity of the block be v

therefore, the initial velocity of the block