The efficiency of a pulley system is 81 percent. The pulleys are used to raise a mass of 85 kg to a height of 8.5 m. The acceleration of gravity is 9.81 m/s^2. What force is exerted on the rope of the pulley system if the rope is pulled for 14 m in order to raise the mass to the required height?
This whole website is useless...:P
To answer this question, we need to calculate the force exerted on the rope of the pulley system. The formula for force can be derived from the work-energy principle:
Force = (Work) / (Distance)
First, let's find the work done by the pulley system. The work done is equal to the force applied multiplied by the distance over which the force is applied:
Work = Force * Distance
We know that the distance is 14 m, so we need to calculate the work done by the system.
Next, we can calculate the work done on the mass:
Work = Force * Distance
The work done on the mass can be calculated as the product of the force acting on the mass and the height through which the mass is raised:
Work = (Force on mass) * (Distance raised)
We know that the mass is 85 kg and the height is 8.5 m. Using the formula for work, we can calculate the work done on the mass.
Now, let's calculate the efficiency of the pulley system. Efficiency is the ratio of useful work output to the work input. In this case, the work input is equal to the work done on the mass, and the useful work output is the work done by the system. Efficiency can be calculated as:
Efficiency = (Useful work output) / (Work input)
We know that the efficiency is 81 percent, which can be written as 0.81. Rearranging the equation, we have:
(Useful work output) = Efficiency * (Work input)
Now we can substitute the values we have and solve for the work done by the system.
Finally, we can calculate the force exerted on the rope of the pulley system using the equation for force:
Force = (Work) / (Distance)
Substitute the values we have and solve for the force exerted on the rope of the pulley system.