To find the mechanical advantage, velocity ratio and efficiency of a single purchase winch crab and plot a graph between W & P and W & efficiency.
Single purchase winch crab, weight, cotton string etc.
It consists of a small wheel gearing with a large wheel , the small wheel is called pinion and the large wheel is called spur wheel. The spur wheel is connected with a load drum of radius (r). One end of rope is fixed to drum and wounded around the drum. The free end of rope carries a load (W). Effort pulley of radius (R) is connected with spindle carrying the pinion. The effort is applied on effort pulley.
W = Load lifted
P = Effort required
R = Radius of effort pulley
r = Radius of load drum
T1 = Number of teeth on pinion
T2 = Number of teeth on spur wheel
In one revolution of effort pulley the distance moved by effort is 2πR (in cm).
For one revolution of load pulley the distance moved by load is 2πr (in cm).
In one revolution of effort pulley the pinion will make one revolution while spur wheel will make [frac up=”T1″ down=”T2″] of a revolution, the load drum will also make [frac up=”T1″ down=”T2″] of revolution.
Distance moved by load = [frac up=”T1″ down=”T2″] x 2πr
Velocity ratio = [frac up=”Distance moved by effort” down=”Distance moved by load drum”]
Velocity ratio = [frac up=”2πrRT” down=”2πr”]
Mechanical Advantage = [frac up=”Load” down=”Effort”] or [frac up=”W” down=”P”]
Efficiency % = [frac up=”Mechanical Advantage” down=”Velocity Ratio”] x 100 or [frac up=”M.A” down=”V.R”] x 100
- Wrap a cotton string around the axle of drum. The string should be wrapped in such a manner that when the effort P is applied the load W is lifted upward.
- Wrap another string around the pulley to carry the effort P.
- Apply a load W on the free end of the string which is coming over the axle of the drum.
- Apply an another load P to the end of the string on effort pulley. Load P should be increased gradually to start the motion of the load upward.
- Note W and P to determine the value of M.A.
|S. No.||Circumference of||No. of teeth||Load Applied
|M.A = [frac up=”W” down=”P”]||V.R =
[frac up=”2πrRT” down=”2πr”]
|Efficiency % = [frac up=”M.A” down=”V.R”] x 100|
- Lubricate the apparatus properly to minimize friction.
- The strings on the pulley and load drum should not overlap.
- Weights should be placed gently on the effort pan.
- The string should be free from knot.