250 N force is required to raise 75 kg mass from a pulley. If rope is pulled 12 m, then the load is lifted to 3 m, the efficiency of pulley system will be
A pulley is a simple machine consisting of a wheel with a rope or chain that passes over it. It changes the direction of force applied to lift heavy objects. Pulleys can be used individually or in systems to reduce the effort needed to raise loads making work easier and more efficient.
Chapter 5 of Class 11 Physics focuses on Work Energy and Power. It explains the concept of work done by a force energy types such as kinetic and potential energy and the principle of conservation of energy. The chapter also covers power as the rate of doing work and explores various practical applications of these concepts in real-world scenarios.
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We use the formula for efficiency of a pulley system:
Efficiency = (Useful Work Output / Total Work Input) × 100
Step 1: Calculate Useful Work Output
Useful work output is the work done in lifting the load. It is given by:
Useful Work Output = Force × Distance lifted
Where,
– Force or weight of the load = mass × gravitational acceleration
– Weight of the load = 75 kg × 9.8 m/s² = 735 N
– Distance lifted = 3 m
Therefore, the useful work output is:
Work Output = 735 N × 3 m = 2205 J
Step 2: Calculate Total Work Input
The total work input is the work done in pulling the rope. This is calculated as:
Total Work Input = Force applied × Distance pulled
Where:
– Force applied = 250 N
– Distance pulled = 12 m
Therefore, the total work input is:
Work Input = 250 N × 12 m = 3000 J
Step 3: Calculate Efficiency
Now, we can find the efficiency:
Efficiency = (Work Output / Work Input) × 100
Efficiency = (2205 J / 3000 J) × 100 ≈ 73.5%
The closest option is 75%.
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