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प्रश्न
A boy lifts a load of 40 kgf through a vertical height of 2m in 5s by using a single fixed pulley when he applies an effort of 48 kgf. Calculate:
(i) the mechanical advantage, and
(ii) the efficiency of the pulley. Why is the efficiency of the pulley is not 100%?
(iii) the energy gained by the load in 5s, and
(iv) the power developed by the boy in raising the load.
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उत्तर
Given:
L = 40 kgf,
dL = 2m,
t = 5 s,
E = 48 Kgf.
(i) Mechanical advantage (M.A.) =`"L"/"E"=40/48=5/6=0.833`
(ii) If the effort moves a distance d downwards, the load also moves a distance d upwards. So velocity ratio (V.R.) = d/d = 1,
Efficiency = `"M.A."/"V.R."=0.833/1`
= 0.833 (or 83.3%).
The efficiency of the pulley is not 100% because some energy is wasted in overcoming the friction in the pulley bearings.
(iii) The energy gained by the load in 5s = Load × Displacement of load in 5s
= 40 kgf × 2m
= 80 kgf × m.
(iv) Power developed by the boy =`"Effort×Displacement of effort"/"Time"=(48"kgf"×2"m")/(5"s")`
= 19.2 kgf × ms−1.
संबंधित प्रश्न
Explain the working of a gear system.
Explain how a gear system can be used to obtain gain in speed? Given one example.
Explain how a gear system can be used to obtain gain in torque? Given one example.
Give reason for the following:
In a single fixed pulley, the velocity ratio is always more than the mechanical advantage.
Give reason for the following:
In case of a block and tackle arrangement, the mechanical advantage increases with the increase in the number of pulleys.
Give reason for the following:
The efficiency of a pulley is always less than 100%
(a) Fig represents an incomplete diagram of a simple string pulley system. Copy this diagram on a new page and complete it and mark where the effort must be applied to lift the load.
(b) What is the velocity ratio of this system?
(c) If the pulley system is 80% efficient and the load is 720 N, then
(i) What effort must be applied to lift the load?
(ii) What work must be done must be done in lifting the load through a distance of 2 m using this machine?
In a single movable pulley system, a load of 125 kgf is lifted by an effort of 75 kgf. Find the percentage efficiency of system.
A pulley system has a velocity ratio of 4 and an efficiency of 90%. Calculate:
(i) the mechanical advantage of the system.
(ii) the effort required to raise a load of 300 N by the system.
A ‘block and tackle’ system used 3 pulleys in the lower block and 4 pulleys in the upper block. What is the ‘velocity ratio’ of this system? If the load is to be lifted by a person capable of applying a maximum effort of 1000 N, what is the maximum load than can be lifted under ideal conditions?
The actual maximum load that gets lifted turns out to be 6300 N. What are the values of the actual M.A. and efficiency of the set-up?
