Question

Conservation of energy

A spring S of force constant k=100 N/m. is fixed to the base of a 30 degree incline.A mass m=50g. is held against the free end of the spring,so that the spring is compressed by 0.1 metre.If the mass is now released,calculate the distance travelled by the mass up the incline.don't ignore friction.
i tried using conservation of evergy theorem but i am not getting the solution.how should i start?

Answer 1

Conservation of energy

A spring S of force constant $k = 100 \, \text{N/m}$ is fixed to the base of a 30 degree incline. A mass $m = 50 \, \text{g}$ is held against the free end of the spring, so that the spring is compressed by 0.1 metre. If the mass is now released, calculate the distance travelled by the mass up the incline. don't ignore friction.

i tried using conservation of every theorem but i am not getting the solution. how should i start?

F- F of friction

Dalambers principle

$Dx = 0.1$ meter - the spring is compressed by 0.1 metre

$Kdx = F + ma + \cos(60) * mg$

$F = b * \sin(60) * mg$

Because $\sin(60) * mg$ is normal force to our incline plane, b-coef of friction

So we have that

$Kdx = b * \sin(60) * mg + ma + \cos(60) * mg$

The mass $m$ will stop when $kdx$ would be greater than $b * \sin(60) * mg + \cos(60) * mg$

From here we can found x:

Cuz $dx = x1 - x0$ x0 is length of spring at rest

$K(x1 - x0) = b * \sin(60) * mg + \cos(60) * mg$

Answer:

$X1 = (b * \sin(60) * mg + \cos(60) * mg + k * x0) / k$