Answer to Question #114189 in Classical Mechanics for Caylin

Question

A spring has a spring constant of 1000N/m. It is compressed by 15cm, then launches a 200g block on a frictionless horizontal surface, it then reaches a 30 DEGREE incline and the blocks coefficient of kinetic friction on incline is 0,20.

What distance 'd' does the block sail through the air?

Please assist.

{ ___d__}
/
[ ] ____/

some type of representation.

Answer 1

As per the given question,

Spring constant$(k)= 1000N/m.$

Compression distance $(x)=15cm$

Mass of the object $(m)=200g=0.2 kg$

Angle of inclination of the plane $(\theta)=30^\circ$

Coefficient of kinetic friction $(\mu)=0.2$

let l is the distance traveled on the inclined plane

Applying the conservation of energy,

$\Rightarrow \dfrac{kx^2}{2}=mg\sin\theta \times l$

$\Rightarrow l =\dfrac{kx^2}{2mg\sin\theta}=\dfrac{1000\times 0.15\times 0.15}{2\times 0.2 \times 9.8 \times \sin 30}$

$\Rightarrow l =\dfrac{225}{1.96}=114.8m$

and height raised by block =57.4m$=l\sin\theta =57.4m$