An arrangement of two pulleys, as shown in the figure, is used to lift a 49.6-kg mass a distance of 3.70 m above the starting point. Assume the pulleys and rope are ideal and that all rope sections are essentially vertical.
(a) What is the mechanical advantage of this system? (In other words, by what factor is the force you exert to lift the weight multiplied by the pulley system?)
(b) What is the change in the potential energy of the weight when it is lifted a distance of 3.70 m?
kJ
(c) How much work must be done to lift the 49.6-kg mass a distance of 3.70 m?
kJ
(d) What length of rope must be pulled by the person lifting the weight 3.70 m higher in the air?
m
Could someone please explain and help me out with this thank you.
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To solve this problem, we will use the principles of pulley systems and work-energy theorem.
(a) The mechanical advantage of a pulley system is equal to the number of rope segments pulling up on the load. In this case, we have two pulleys and three rope segments pulling up on the load. Therefore, the mechanical advantage is 3.
(b) The potential energy of an object is given by the equation PE = mgh, where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height. In this case, the mass is 49.6 kg and the height is 3.70 m. Substituting the values into the equation, we have: PE = 49.6 kg * 9.8 m/s² * 3.70 m = 1,783.04 J. However, the answer is expected in kJ, so we convert J to kJ by dividing the value by 1000. Therefore, the change in potential energy is 1.78304 kJ.
(c) The work done to lift an object is equal to the change in potential energy. Therefore, the work done to lift the 49.6-kg mass a distance of 3.70 m is also 1.78304 kJ.
(d) To determine the length of the rope that needs to be pulled, we can use the principle of the conservation of rope in a pulley system. In this case, the length of rope pulled by the person lifting the weight is equal to the distance the weight has been lifted. Therefore, the length of the rope pulled is 3.70 m.