(a) Find the speed of the block at the equilibrium point. ? m/s (b) Find the spe

Question

(a) Find the speed of the block at the equilibrium point.
?   m/s

(b) Find the speed when x = 0.029 m.
?   m/s

(c) Repeat part (a) if friction acts on the block, with coefficient ?k = 0.170.

?   m/s

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?
?   m

(b) How does the answer change if the coefficient of kinetic friction is ?k = 0.170? (Use the quadratic formula.)

Explanation / Answer

here,

mass of the block , m = 5.02 kg

k = 348 N/m

xi = 0.051 m

(a)

let the speed at the equilibrium point be v

using the conservation of energy

0.5 * m * v^2 = 0.5 * k * x^2

5.02 *v^2 = 348 * 0.051^2

v = 0.42 m/s

the speed at the equilibrium point is 0.42 m/s

(b)

let the speed at x' = 0.029 m

using the conservation of energy

0.5 * m * v^2 = 0.5 * k * x^2 - 0.5 * k* x'^2

5.02 *v^2 = 348 * 0.051^2 - 348 * 0.029^2

v = 0.35 m/s

the speed at x = 0.029 m is 0.35 m/s

(c)

uk = 0.17

let the speed at the equilibrium point be v

using the conservation of energy

0.5 * m * v^2 = 0.5 * k * x^2 - uk *m*g*x

5.02 *v^2 = 348 * 0.051^2 - 0.17 * 5.02 * 9.8* 0.051

v = 0.31 m/s

the speed at the equilibrium point is 0.31 m/s

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