# A particle of mass 1 kg is given a horizontal velocity of 4 m/s along a horizontal surface, with which it has a coefficient of friction (both static and kinetic) of  0.4. The particle strikes a fixed ideal spring of force constant 6 N/m after travelling a distance of 0.25 m. Assume acceleration due to gravity is 10 m/s 2 . Find the final displacement of the particle from its starting point

Arun Kumar IIT Delhi
10 years ago
Hi
I saw your attached image and last image figure seems to represent your problem.
Since you haven't mentioned when in the question i'll find the displacement till it stops the first time.

$\\gain in PE+work done by friction and =loss in kinetic energy \\\frac{1}{2}kx^2+(x+0.25)*0.4*mg=\frac{1}{2}mv^2 \\=>\frac{1}{2}6x^2+(x+0.25)*4=\frac{1}{2}4^2 \\=>3x^2+4(x+0.25)=8 \\=>3x^2+4x=7 \\=>x=\frac{-4 \pm \sqrt{16+84}}{6} \\=>x=1 \\final displacement = 1+0.25=1.25m$

Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty

Shravan soni
13 Points
2 years ago
A particle of mass 1 kg is given a horizontal velocity 4ms along a horizontal surface with it has a coefficient of friction both statically kinetic of 0.4 the particle strike a fixed ideal spring of force constant 6 n per m after traveling a distance of0.25m assume acceleration