Question

A 1.0 kg block of wood is to be launched across a slippery floor by a compresssed spring. The stiffness constant of the spring is 100 N/m, and the spring is initially compressed by 0.50 meters. If the block slides 10 meters before coming to rest, what is the coefficient of sliding friction? If the block were to slide 0.50 meters - the very same distance the spring was compressed - what would be the coefficient of sliding friction?

Answer 1

given that

m = 1 Kg and K = 100N/m and initial compression in the spring = 0.5m = x₁

Block slides 10m before coming to rest, therefore, by energy balancing:

the initial potential energy of spring = energy lost due to friction

=> 0.5*K*x₁² = *Mgx

where x = 10+0.5 = 10.5m

0.5*100*(0.5)² = *1*10*10.5

=> = 0.12

now, if the block were to slide only 0.5m then using the above relation

coffecient of friction would be equal to 2.5, which is practically not possible.