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
To find the answers to these questions, we can use the principles of mechanical advantage and work done.
(a) The mechanical advantage of the pulley system can be calculated using the formula:
Mechanical Advantage = (Force applied to the system) / (Force applied to lift the weight)
In this case, the force you exert is the force applied to the system, and the weight of the object is the force applied to lift the weight. Since the weight is being lifted vertically and the pulleys are assumed to be ideal, the force applied to lift the weight will be equal to the weight of the object (mg), where m is the mass and g is the acceleration due to gravity.
So, the mechanical advantage can be calculated as:
Mechanical Advantage = (Force applied to the system) / (mg)
To find the force applied to the system, we divide the weight of the object by the mechanical advantage:
Force applied to the system = (mg) / Mechanical Advantage
Given:
Mass (m) = 49.6 kg
Acceleration due to gravity (g) = 9.8 m/s^2
We need to know the arrangement of the pulleys in order to determine the mechanical advantage. Please provide additional information about the pulley system.
(b) The change in potential energy of the weight can be calculated using the formula:
Change in Potential Energy = mgh
Where m is the mass, g is the acceleration due to gravity, and h is the height or distance. In this case, h is given as 3.70 m. Plug in the given values to find the change in potential energy in joules.
(c) The work done to lift the mass can be calculated using the formula:
Work Done = Force * Distance
In this case, the force is the weight of the object (mg) and the distance is given as 3.70 m. Plug in the given values to find the work done in joules.
(d) To find the length of rope that must be pulled by the person lifting the weight, we need to know the arrangement of the pulleys. The length of rope pulled will depend on how the pulleys are arranged. Please provide additional information about the pulley system.