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

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 vi = 3.10 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 distance d. The 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. a. Find the distance of compression d. b. Find the speed v at the unstretched position when the object is moving to the left. c. Find the distance D where the object comes to rest.

Explanation / Answer

Friction force = FF FF = 0.250 x Normal force Normal force = weight of mass = mg = (1.20)(9.81) = 11.77 N FF = 0.250(11.77) = 2.942 N Work done by FF = 2.942D mass stops when Work by FF = K.E. mass as it leaves spring 2.942D = 1/2mv² 2.942D = 1/2(1.20)(3.10)² D = (0.5)(1.10)(3.30)²/2.942 D = 5.766/2.942 D = 1.96 m....................... ANS

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