PRACTICE IT Use the worked example above to help you solve this problem. A block

Question

PRACTICE IT Use the worked example above to help you solve this problem. A block with mass of 5.86 kg is attached to a horizontal spring with spring constant k 3.82 x 102 N/m, as shown in the figure. The surface the block rests upon is frictionless. The block is pulled out to x' = 0.0470 m and released (a) Find the speed of the block at the equilibrium point. 0379m/s (b) Find the speed when x = 0.033 m 0.27 m/s (c) Repeat part (a) if friction acts on the block, with coefficient .155 m/s -0.130. EXERCISE HINTS: GETTING STARTED I'M STUCK! Use the values from PRACTICE IT to help you work this exercise. Suppose the spring system in the last example starts at x 0 and the attached object is given a kick to the right, so it has an initial speed of 0.5 m/s (a) What distance from the origin does the object travel before coming to rest, assuming the surface is frictionless? 0.062 (b) How does the answer change if the coefficient of kinetic friction is & = 0.1307( Use the quadratic formula.) 0.16 When friction is present, do you expect the distance to be larger or smaller than when friction is not present? m Need Help? Read It

Explanation / Answer

from work energy relation

total work = dKE

We + Wf = Kf - Ki

Uei - Uef + Wf = Kf - Ki

0 - (1/2)*k*x^2 - uk*m*g*x = 0 - (1/2)*m*v^2

-(1/2)*3.82*10^2*x^2 - 0.13*5.86*9.8*x = -(1/2)*5.86*0.5^2

x = 0.045 m

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