A classical mechanics problem by Prakhar Bindal

Classical Mechanics Level 5

A block of mass 1 kg is given a horizontal velocity of 4 m/sec along a horizontal surface which provides a

coefficient of friction of 0.4 (both kinetic and static) . the block strikes a fixed horizontal ideal spring of force

constant 6N/m after travelling a distance of 0.25 m along the horizontal surface .

Find the final displacement of the block from its starting point.

If your answer can be expressed as a/b where a and b are positive coprime integers then find the value of (a*b) + 30

Details And Assumptions

assume that the natural length of the spring is sufficient for the block to fully come to rest ( neglect any collision )

friction is present everywhere on the horzontal surface (even on that surface too where the spring is present)

assume Acceleration due to gravity = 10 SI units

The spring is ideal (massless , does not possess its own kinetic energy)

the answer should be calculated in SI units only .

The answer is 114.

1 solution

Aryan Goyat
Nov 28, 2015

The question is easy but a tricky one. first we conserve energy and we get--- m=1,v=4,f=4----- 1/2(m)(v v)=1/2 (k) square(x)+f(0.25)+f(x)--- we get x=1,but it will not be at equilibrium at this instant 6(1)>4--- so the block will move opposite side. again we equate the work done by friction and energy lost by spring. 3(1)-3(1-x) (1-x)=4x--------------------------------------------------------------------------------------- we get x=(2/3)-------------------------------- total displacement=1+0.25-2/3=7/12--------------------------------

prakhar you must try aryan coordinate challenge #1 you will find it interesting if you would have not done it before.