A book with mass 2.90 kg is attached to a spring. The spring has force constant

Question

A book with mass 2.90 kg is attached to a spring. The spring has force constant k= 290 N/m and negligible mass. The spring gets compressed x=0.300 m. The book is released and slides along å surface with kinetic friction coefficient 0.3.

a) If the spring and the surface are horisontal, how far from the starting point ( when the spring is compressed) will the book slip before it stops?

b) If the spring had been mounted on a slope instead with an angel 30 degrees, how far from the starting point has the book slipped before og stops?

Explanation / Answer

given

mass of book, m = 2.9 kg

force constant of the spring = k = 290 N/m

xo = 0.3 m

muk = 0.3

a. when the spring is compressed, energy stored U = 0.5kxo^2

U = 13.05 J

this energy is converted to heat by friction

hence

distnace covered beofre stopping = x

hence from conservation of enregy

muk*mg*x = 13.05

x = 1.52905 m

b. if the spring is mounted on a slope with angle theta = 30 deg

then

from conservation of ernegy

13.05 = muk*mg*cos(30)*x + mgx*sin(30)

x = 0.6037259 m

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