C5Worksheet - A certain spring hanging from the ceiling has...

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A certain spring hanging from the ceiling has a force constant k = 50 N/m and a natural length l o = 20 cm. A 0.5-kg mass is attached to the spring, and the mass is lifted so that the spring is 10 cm long. The mass is then released from rest. 1) How much potential energy is stored in the spring before the mass is released? Answer: 0.250 J 2) What force does the spring exert on the mass before it is released? Answer: 5.00 N [down] 3) What is the acceleration of the mass at the instant it is released? Answer: 19.8 m/s 2 [down] 4) How much has the spring stretched when the net force on the mass is zero? (This is when the mass is “in equilibrium.”) How long is the spring at that instant? Answer: stretch = 9.80 cm; length = 29.8 cm 5) What is the speed of the mass when it is in equilibrium? (The answer is not zero.) Answer: 1.98 m/s 6) What is the speed of the mass when the spring is again 20-cm long? Answer: 1.72 m/s 7) What is the maximum stretch of the spring? What is the maximum length of the spring? Answer: 29.6 cm, 49.6 cm 8) If the maximum length of the spring is 40 cm, what average friction force opposes the motion of the mass? Answer: 2.40 N [up] A 50-kg mass on a smooth surface is released from rest from the position shown. It is pulled up and to the right by force F = 50 N and horizontally to the left by a spring. The spring has force constant k = 50 N/m and unstretched length l o = 0.10 m. 9) What is the potential energy initially stored in the spring? Answer: 4.00 J 10) If the mass moves forward 0.5 m, how much work is done by force F ? Answer: 20.5 J 11) If the mass moves forward 0.5 m, how much work is done on the spring?
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