Question

calculate example 6.8 taking the coefficient of friction to be 0.5 and calculate the maximum compression of the spring

Answer 1

Answer:

5 rounds isanswer to the question

Answer 2

Answer:

Explanation:

In the presence of friction, both the spring force and the frictional force "f" act so as to oppose the compression of the spring.

Work done by the two forces :

W = −1 / 2 kx^2 m − f(xm)

W = − 1/2 kx^2 m − μmg(xm)

(Since f = μR = μmg)  

Change in K.E

ΔK = Kf − Ki = 0 −1/2 mv^2

Applying work energy theorem, ΔK = W

− 1 / 2 mv^2 = −1 / 2 kx^2 m − μmg(xm)

kx^2 m + 2μmg (xm) − mv^2 = 0  

It is a quadratic equation in xm

xm = −2 μmg + [4μ^2.m^2.g^2 + 4.m.kv^2]^1/2 / 2k

Putting the numerical values we get "m" = 1.35 m

Hence the maximum compression of the spring is "m" = 1.35