Rupert is investigating the properties of a light (effectively massless) spring.
ID: 2189673 • Letter: R
Question
Rupert is investigating the properties of a light (effectively massless) spring. He has attached one end of the spring to a fixed horizontal rod and allowed the spring to hang vertically. The free end of the spring has a small hook to which Rupert can attach various masses. Rupert finds that if he attaches a 500 gram mass to the hook, and then very slowly lowers the mass with his hand until the force on the mass by the spring is as large as the weight of the mass, that the spring stretches by 32 cm. (a) What is the spring constant of Rupert's spring? N/m The 500 mass is now hanging from the end of the spring. Rupert grasps the mass with his hand and pulls it down by 18 cm. He then releases the mass from rest. You will be asked to find the speed of the mass after it has moved upwards by 18 cm from its release point. First, answer these preliminary questions. What is the force on the mass by the spring at the instant after Rupert releases his grip on the mass? What is the weight of the hanging mass? What is the net force on the mass at the instant after Rupert releases his grip on the mass? And what is the acceleration of the mass at the instant after Rupert releases his grip on the mass?Explanation / Answer
mg = kx
0.500 x 9.81 = k(0.32)
k = 15.33 N/m
F = kx = 15.33 x (0.18) =2.76 N upwards
W = 0.500 x 9,.81 = 4.9 N downeards
Fnet = 4.9 - 2.76 = 2.145 N downwards
a = Fnet / m = 2.145/0.5 =4.29 m/s2
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