Finding coefficient of kinetic friction on a 30° incline using energy conservation

[RayanLhindi]

1. Homework Statement
m = 4.00 kg
theta = 30
v = 1 m/s
compression of the spring by the block , x = 0.3 m
d = 5 m

Homework Equations

rule : Fk = μ k * N
i must find Fk first to find μ k using conservation energy, [/B]

The Attempt at a Solution

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.

 

[andrewkirk]

You don't appear to have used the data from the first part of the experiment - on the horizontal frictionless surface. The purpose of the first part is to allow you to calculate the spring constant using conservation of energy techniques. You can then use the spring constant to solve the second part on the frictional, inclined surface.

PS: The spring constant K that you calculate above is not correct. It's much easier to calculate it using the horizontal info - and hence less likely to generate errors.

 

[RayanLhindi]

You don't appear to have used the data from the first part of the experiment - on the horizontal frictionless surface. The purpose of the first part is to allow you to calculate the spring constant using conservation of energy techniques. You can then use the spring constant to solve the second part on the frictional, inclined surface.

PS: The spring constant K that you calculate above is not correct. It's much easier to calculate it using the horizontal info - and hence less likely to generate errors.

I will check the spring constant again no problem, but the first part how to solve it ? Can you give me a hint ? Cuz I am so confused now if all this calculations is for nothing :(

 

[andrewkirk]

To solve for the spring constant write an equation that equates the block's KE from the horizontal case, when not in contact with the spring the spring, with the PE of spring compression at maximum compression. One of those two amounts involves K and all other quantities in the two amounts are known, so you can solve for K.

 

[haruspex]

F = ma
F = 4 * 9.81 = 39.24N
KE = 0.5 mv^2
KE = 0.5 * 39.24 * 1^2 = 19.62J

You calculated a force, F (what force do you think this is?) then appear to have used the resulting number as though it is a mass.