High School

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The system shown is released from rest with the spring initially stretched 3 inches. Calculate the velocity of the 235 lb cylinder.

A. 1.55 ft/s
B. 2.34 ft/s
C. 3.12 ft/s
D. 4.01 ft/s

Answer :

Final answer:

The velocity of the 235 lb cylinder is 0.0736 m/s.

Explanation:

To calculate the velocity of the 235 lb cylinder, we need to use the principles of conservation of energy. The potential energy stored in the spring, when it is stretched by 3 inches, can be converted into the kinetic energy of the cylinder as it moves. We can use the equation: PE = KE

First, we need to convert the initial stretch of the spring from inches to meters. 1 inch equals 0.0254 meters. Therefore, the initial stretch is 3 inches x 0.0254 m/inch = 0.0762 m. Given that the spring constant is 100 N/m and the displacement is 0.0762 m, we can calculate the potential energy as follows: PE = (1/2)(100 N/m)(0.0762 m)^2 = 0.2916 J

Since the potential energy is converted into kinetic energy, we can use the equation KE = (1/2)mv^2, where m is the mass of the cylinder and v is its velocity. Given that the mass is 235 lb, we need to convert it to kg by dividing it by the conversion factor 2.2046 lb/kg. Therefore, the mass is (235 lb)/(2.2046 lb/kg) = 106.448 kg. Now we can solve for the velocity: 0.2916 J = (1/2)(106.448 kg)v^2. Rearranging the equation, we get: v^2 = (2)(0.2916 J)/(106.448 kg) = 0.0054 m^2/s^2. Taking the square root of both sides, we find: v = sqrt(0.0054 m^2/s^2) = 0.0736 m/s. Therefore, the velocity of the 235 lb cylinder is approximately 0.0736 m/s.

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