A block of mass 1.9 kg is attached to one end of a spring, the other end of whic

Question

A block of mass 1.9 kg is attached to one end of a spring, the other end of which is tethered to the wall. The spring is stretched by a length 0.13 m and let go, so that the ball slides across the floor. The coefficient of friction between the block and the floor is 0.41. The spring constant is 679 N/m. a) What is the kinetic energy of the block at the instant tto when the spring is unstretched? b) The block keeps going after this, and the spring is compressed. When the block comes to rest (for the first time for t > to), the spring has been compressed by a length a. Obtain an expression for the frictional work done from the instant t = to up to this point, and the potential energy at this point. Use these expressions, conservation of energy, and the answer to part a) to solve for z. (Your answer should be positive.)

Explanation / Answer

a) conserving energy

Initial energy of spring=final kinetic energy+energy lost in friction

0.5*k*x*x=0.5*m*v*v+0.41*mg*0.13

We got

v=2.23 m/s

Kinetic energy=4.72 J

b)

Work done by friction=0.41*1.9*9.8*x=7.63x

Potential energy=0.5*679*x^2=339.5x^2

Conserving energy

0.5*1.9*2.23^2=4.72=7.63x+339.5x^2

We got

x=0.107

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