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
Please someone help me out thank you.
To solve this problem, we need to use the principle of work and energy and analyze the pulley arrangement.
(a) The mechanical advantage of this system can be determined by counting the number of ropes supporting the weight. In this case, there are two ropes supporting the weight. Each rope contributes a mechanical advantage of 2. Therefore, the total mechanical advantage is 2 * 2 = 4.
(b) The change in potential energy can be calculated using the formula:
ΔPE = m * g * h
where ΔPE is the change in potential energy, m is the mass, g is the acceleration due to gravity, and h is the height or distance lifted. Plugging in the given values:
ΔPE = 49.6 kg * 9.8 m/s^2 * 3.70 m = 1817.04 Joules (J)
To convert Joules to kilojoules (kJ), divide by 1000:
ΔPE = 1817.04 J / 1000 = 1.81704 kJ
(c) The work done to lift the mass can be calculated using the formula:
W = F * d
where W is the work done, F is the force applied, and d is the distance lifted. In this case, the force applied is equal to the weight of the mass (mg). Therefore:
W = m * g * d
Plugging in the given values:
W = 49.6 kg * 9.8 m/s^2 * 3.70 m = 1785.376 Joules (J)
Converting Joules to kilojoules (kJ):
W = 1785.376 J / 1000 = 1.785376 kJ
(d) To determine the length of rope pulled by the person lifting the weight, we need to consider the total distance lifted by the weight. In this case, the weight is lifted 3.70 m above the starting point. Since the rope sections are essentially vertical, the length of the rope pulled will be equal to the distance lifted by the weight:
Length of rope pulled = 3.70 m