To use the equations of equilibrium to find unknown forces in two dimensions: un

Question

To use the equations of equilibrium to find unknown forces in two dimensions: understand the relationship between a spring's unloaded length, its displacement, and its loaded length; and use the spring equation to solve problems involving multiple springs. As shown, a frictionless pulley hangs from a system of springs and a cable. The pulley is equidistant between the two supports attaching the spring to the ceiling. The distance between the supports is d = 1.50 m. The cable cannot stretch and its length between the two springs is 1.8 m. Finding an unknown weight As shown, a mass is hung from the pulley. This mass causes a tensile force of 15.0 N in the cable and the pulley to hang h = 130.0 cm from the ceiling. Assume that the pulley has no mass. What is the weight of the mass? Express your answer to three significant figure and include the appropriate units. Finding the mass of the pulley As shown, an object with mass m = 6.0 kg is hung from a pulley cannot be massless as assumed. Find the mass of the pulley. Express your answer to three significant figures and include the appropriate units. For this problem, use g = 9.81 m/s2.

Explanation / Answer

1) neglecting mass of pulley the attached mass, M is given by
2*15*cos{arctan(75/130)} = M*9.81

2) Not neglecting mass of pulley, the mass of pulley is given by
2*43.5*cos{arctan(75/147.2)} = x
(x +m)*9.81 or m+5.1 = 7.1 kg or m = 2 kg

Please do calculations

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