Question

A man raises a load of weight 1200N by using a system of pulleys (a three pulley system ).He exerts a force of 300N on the rope.Find (a) the velocity ratio; (b) the mechanical advantage; (c) the efficiency of the system. Also, state one reason why the efficiency of the system is less than 100%.

Answer 1

Answer:

Part a)

Velocity ratio is 1 : 4

Part b)

mechanical advantage is 4

Part c)

efficiency is 75% and its less than 1 because of energy loss

Explanation:

Part a)

As we know that the Power output and power input must be same

So we will have

$F_{in}v_{in} = F_{out}v_{out}$

$1200 v_1 = 300 v_2$

$\frac{v_1}{v_2} = \frac{300}{1200}$

$\frac{v_1}{v_2} = \frac{1}{4}$

Part b)

As we know that mechanical advantage is ratio of output force and input force

So we will have

$MA = \frac{F_{out}}{F_{in}}$

$MA = \frac{1200}{300}$

$MA = 4$

Part c)

efficiency of the system is given as

$Efficiency = \frac{N}{MA}$

so we will have

$\eta = \frac{3}{4}$

$\eta = 75$%

here efficiency is less than 100% because there is loss of energy always in this case

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Topic : Mechanical advantage

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Answer 2

(a) The velocity ratio is 3

(b) The mechanical advantage is 4

(c) The efficiency of the system is 75%

Given:

Load = 1200 N

Effort = 300 N

Number of pulleys = 3

Explanation:

(a) Number of pulleys = Velocity ratio

∴ Velocity ratio = 3

(b) The mechanical advantage is given by the formula:

Mechanical advantage = Load/Effort

On substituting the values, we get,

Mechanical advantage = 1200/300

∴ Mechanical advantage = 4

(c) The efficiency is given by the formula:

η = Efficiency = (Velocity ratio)/(Mechanical advantage)

On substituting the values, we get,

η = 3/4 =

η = 0.75

∴ η = 0.75 × 100% = 75%

The efficiency of a system can never be 100% because there are loss of energy and loss due to friction and lubrication.