A block and tackle system of pulleys consisting of 5 pulleys is used to raise a load of 500 N through a height of 12m. If the total work done by the system is 7200 J. calculate the 1. Work done against friction 2. Efficiency of the system
A block and tackle system of pulleys consisting of 5 pulleys is used to raise a load of 500N through a height of 12m. If the total work done by the system is 7200j calculated the work done against friction and calculated the efficiency of the system
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Please solve the calculation
Need answer to question. A block and tackle system of pulleys consisting of 5 pulleys is used to raise a load of 500 N through a height of 12m. If the total work done by the system is 7200 J. calculate the 1. Work done against friction 2. Efficiency of the system
To calculate the work done against friction and the efficiency of the system, we need to understand the concept of work, mechanical advantage, and efficiency in relation to pulley systems.
1. Work done against friction:
The work done against friction can be calculated by subtracting the work done by the system from the total work done.
Work done by the system = force * distance
Work done by the system = 500 N * 12 m = 6000 J
Work done against friction = Total work done - Work done by the system
Work done against friction = 7200 J - 6000 J = 1200 J
So, the work done against friction is 1200 J.
2. Efficiency of the system:
Efficiency is a measure of how well a system converts input work to useful output work. In a pulley system, efficiency can be calculated using the formula:
Efficiency = (Useful work output / Total work input) * 100%
To calculate the efficiency, we need to determine the useful work output and the total work input.
Useful work output: This refers to the work done on the load. In this case, the work done on the load is equal to the total work done by the system.
Total work input: This represents the work done by the person or the input force. It can be calculated by multiplying the input force applied by the distance the force acts through.
Total work input = Input force * Distance
In this case, the distance is the same as the height raised, which is 12 m. The input force depends on the mechanical advantage of the system.
Mechanical advantage is the factor by which the pulley system multiplies the input force applied. In a block and tackle system with 5 pulleys, the mechanical advantage can be calculated as follows:
Mechanical advantage = 2^(Number of movable pulleys)
Mechanical advantage = 2^5
Mechanical advantage = 32
The input force can be calculated by dividing the load by the mechanical advantage:
Input force = Load / Mechanical advantage
Input force = 500 N / 32 ≈ 15.625 N
Total work input = Input force * Distance
Total work input = 15.625 N * 12 m = 187.5 J
Efficiency = (Useful work output / Total work input) * 100%
Efficiency = (6000 J / 187.5 J) * 100%
Efficiency ≈ 3200%
Therefore, the efficiency of the system is approximately 3200%.