A 2.95 kg block on a horizontal floor is attached to a horizontal spring that is

Question

A 2.95 kg block on a horizontal floor is attached to a horizontal spring that is initially compressed 0.0300 m . The spring has force constant 900 N/m . The coefficient of kinetic friction between the floor and the block is 0.45 . The block and spring are released from rest and the block slides along the floor.

Part A

What is the speed of the block when it has moved a distance of 0.0200 m from its initial position? (At this point the spring is compressed 0.0100 m .)

Express your answer with the appropriate units.

Explanation / Answer

here,

mass of the block , m = 2.95 kg

spring constant , k = 900 N/m

initially compression , x = 0.03 m

final compression , x' = 0.01 m

the coefficient of friction , uk = 0.45

let the speed of the block be v

using conservation of energy

0.5 * k * x^2 = 0.5* k * x'^2 + 0.5 * m * v^2 + ff * ( x - x')

0.5 * 900 * 0.03^2 = 0.5 * 900 * 0.01^2 + 0.5 * 2.95 * v^2 + 0.45 * 2.95 * 9.8 * ( 0.03 - 0.01)

v = 0.26 m/s

the speed of the block when it moved a distance of 0.02 m from initial position is 0.26 m/s

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