In the figure, a 3.3 kg block is accelerated from rest by a compressed spring of

Question

In the figure, a 3.3 kg block is accelerated from rest by a compressed spring of spring constant 630 N/m. The block leaves the spring at the spring's relaxed length and then travels over a horizontal floor with a coefficient of kinetic friction k-0.214. The frictional force stops the block in distance D = 7.7 m, what are (a) the increase in the thermal energy of the block-floor system, (b) the maximum kinetic energy of the block, and (c) the original compression distance of the spring? No friction- D- (Hk)

Explanation / Answer

a) the wor done by the friction is the increase in the thermal energy of the block-floor system

the frictional work is given by

wf = k*m*g*D

where k = coefficient of friction= 0.214

m= mass =3.3 kg

g= 9.8 m/s2

and D= distance = 7.7 m

hence

wf = k*m*g*D = 0.217*3.3*9.8*7.7 = 54.04 Joules

b) the maximum kinetic energy (Ek) of the block is the increase in the thermal energy = 54.04 Joules

c) we know that

Ek = kx2 /2

which implies that

x= sqrt(2*Ek/k) =sqrt(2*54.04/630) = 0.414 m

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