# Finding the spring constant and the distance of the block?

the question is too long, i couldn't write it or upload it in Yahoo uploader,

this is the link of it : http://d.top4top.net/p_86ub1h1.png

m = 4.00 kg

theta = 30

v = 1 m/s

compression of the spring by the block , x = 0.3 m

d = 5 m

rule : Fk = μ k * N

i must find Fk first to find μ k using conservation energy,

First find N,

N = m x g x cos theta

N = 4 * 9.81 * cos30 = 33.98N

then we find the force to find the spring constant

F = ma

F = 4 * 9.81 = 39.24N

KE = 0.5 mv^2

KE = 0.5 * 39.24 * 1^2 = 19.62J

PE = 0.5 kx^2 => 0.5 Fx

PE = KE

0.5 Fx = 0.5 mv^2

x = v^2 / a = 1^2 / 9.81 = 0.101m

K = f/x = 392.4

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Here i am confused, our professor told us to use mechanical energy and conservation energy to find Fk ,

and the rules is

delta E = delta E mechanics + delta E thermo + delta E internal

K2 + U2 = K1 + U1

The question is long and very tricky, i solve what i can, and i not sure about it actually, if you can help me i will be very thankful.

Relevance

I question a couple of your steps:

(i) F = 4 * 9.81 = 39.24N

Why do this? This is the weight of the object.

(ii) KE = 0.5 * 39.24 * 1^2 = 19.62J

This is wrong. You have put the weight in instead of the mass.

(iii) delta E = delta E mechanics + delta E thermo + delta E internal

That looks OK, but

K2 + U2 = K1 + U1

has lost something. Instead, you should wind up with

deltaE = deltaThermo = friction work = initial GPE - final SPE

since the deltaKE is zero.

spring PE becomes block KE

½kx² = ½mv² → ½ cancels

k * (0.20m)² = 4.00kg * (1.00m/s)²

k = 100 N/m

Simple enough.

Now consider the incline problem:

initial GPE = friction work + final SPE

m*g*(5.00m + 0.30m)*sinΘ = µ*m*g*(5.00m + x)*cosΘ + ½k(0.3m)²

Plug in m, g, k and Θ and solve for µ.

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