Advertisements
Advertisements
Question
A pulley system with VR = 4 is used to lift a load of 175 kgf through a vertical height of 15 m. The effort required is 50 kgf in the downward direction. (g = 10 N kg-1)
Calculate:
- Distance moved by the effort
- Work done by the effort
- M.A. of the pulley system
- Efficiency of the pulley system
Advertisements
Solution
1) Displacement due to the effort is VR = 4
Load (L) = 175 kgf
Effort (E) = 50 kgf
Load displacement (dL) = 15 m
`VR = d_E/d_L`
Effort displacement (dE) = 4 × dL
= 4 × 15
= 60 m
Distance moved by the effort is 60 m
2) Work done by the effort is calculated using the following formula.
Work done by effort (WE) = `"Force"_"Effort" xx d_E`
WE = 50 × 60
= 3000 J
3) Mechanical advantage of the pulley system is calculated as
MA of the pulley system = `"Load (L)"/"Effort (E)"`
= `175/50`
= 3.5
4) Efficiency of the pulley is the ratio of work output to the work input required by the system
Efficiency of the pulley system (η) = `"Work output (Work Done by Load)"/"Work input (Work Done by Effort)"`
Work done by load = ForceLoad x dL
= 175 × 15
= 2625 kgf
:. η = `2625/3000`
= 0.875 × 100
= 87.5 %
APPEARS IN
RELATED QUESTIONS
What is a pulley?
Explain how a gear system can be used to obtain gain in speed? Given one example.
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.
Name the type of single pulley that can act as a force multiplier. Draw a labeled diagram of the pulley mentioned by you.
Draw the diagram of a single movable pulley and obtain its mechanical advantage, velocity ratio, and efficiency.
The alongside figure shows the combination of a movable pulley P1 with a fixed pulley P2 used for lifting up a load W.
(i) State the function of the fixed pulley P2.
(ii) If the free end of the string moves through a distance x, find the distance by which the load W is raised.
(iii) Calculate the force to be applied at C to just raise the load W = 20 kgf, neglecting the weight of the pulley P1 and friction.
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?
| Meera chose to use a block and tackle system of '9' pulleys instead of a single movable pulley to lift a heavy load. |
Why should she connect more number of pulleys in the upper fixed block?
A block and tackle system of pulleys has a velocity ratio of 4.
- Draw a labelled diagram of the system indicating clearly the direction of the load and effort.
- Calculate the potential energy of the load 100 kgf lifted by this pulley to a height 5 m. (g = 10 ms−2)
