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A 1.20 kg object slides to the right on a surface having a coefficient of kineti

ID: 1790358 • Letter: A

Question

A 1.20 kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Fig. P7.54). The object has a speed of V; = 3.50 m/s when it makes contact with a light spring that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distancedThe object is then forced toward the left by the spring and continues to move in that direction beyond the spring's unstretched position. The object finally comes to rest a distance D to the left of the unstretched spring. - Tamine Imme d IY = 0 VVVVVVVV v = 0 D-HAWWWWW Figure P7.54 (a) Find the distance of compression d. (b) Find the speed v at the unstretched position when the object is moving to the left. m/s (c) Find the distance D where the object comes to rest.

Explanation / Answer

a) KEi = W + P E

1/2 * 1.20 * 3.52 = (0.25 * 1.20 * 9.8 * d ) + (0.5 * 50 * d2)

7.35 = 2.94 d + 25 d2

d = 0.486 m

b) 1/2 m v2 - 1/2 m vi2 = -f (2 d)

v = sqrt [vi2 - (4 mu m g * d) / m]

= sqrt [vi2 - (4 mu m g * d) / m] = sqrt [vi2 - 4 mu g d]

= sqrt [3.52 - (4 * 0.25 * 9.8 * 0.486)]

speed = 2.74 m/s

c) distance D = vi2 / 2 mu g - 2 d

= [3.52 / (2 * 0.25 * 9.8)] - (2 * 0.486)

D = 1.53 m