When a 0.20-kg mass is suspended from a vertically hanging spring, it stretches
ID: 2168848 • Letter: W
Question
When a 0.20-kg mass is suspended from a vertically hanging spring, it stretches the spring from its original length of3.0cm to a total length of6.0cm. The spring with the same mass attached is then placed on a horizontal frictionless surface. The mass is pulled so that the spring stretches to a total length of 10.0 cm; then the mass is released and it oscillates back and forth (the figure below). What is the maximum speed of the mass as it oscillates?
When a 0.20-kg mass is suspended from a vertically hanging spring, it stretches the spring from its original length of3.0cm to a total length of6.0cm. The spring with the same mass attached is then placed on a horizontal frictionless surface. The mass is pulled so that the spring stretches to a total length of 10.0 cm; then the mass is released and it oscillates back and forth (the figure below). What is the maximum speed of the mass as it oscillates?Explanation / Answer
Let: m be the mass, g be the acceleration due to gravity, k be the spring constant, x be the extension, w be the angular frequency, a be the amplitude, v be the maximum speed. When the mass is hung on the vertical spring: mg = kx k = mg / x ...(1)=k/m=g/x The angular frequency of the SHM is: w = sqrt(k / m) v = wa = a sqrt(k / m) Substituting for k from (1): v = a sqrt(g / x) = 0.03 sqrt(9.81 / 0.05) = 0.42 cm/sec.
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