Question

P is the pull required to lift a load W by means of a pulley block, find a linear law of the form P = mW + C, connecting P and W , using the following data. P (in kg.) 12 15 21 25 W (in kg.) 50 70 100 120

Answer 1

Given :

The pull required to lift a load W by means of a pulley block = P

Given values of P in kg :

12  , 15 , 21 , 25

Corresponding values of W in kg :

50 , 70 , 100 , 120

To Find :

A linear law relating P and W of the form :

P = mW + C

Solution :

Since the values of P and W are given , so on putting the corresponding values we can find the values of m and C .

When P = 12  and W = 50 :

12 = 50m + C   - (1)

When P = 15 and W = 70    

15 = 70m + C   -(2)

Subtracting eq (1) from eq (2) :

15 - 12 = m( 70 - 50 ) + C - C  

Or, 3 = 20m

Or, m = $\frac{3}{20}$

Now putting m = $\frac{3}{20}$  in eq (1):

$12 = \frac{3}{20}\times 50 + C$

Or, $C = 12 -\frac{15}{2}= \frac{9}{2}$

So, the expression of linear law becomes :

$P = \frac{3}{20}.W + \frac{9}{2}\\20 P = 3W + 90$

Hence the linear law relating P and W is :

20P = 3W + 90

Answer 2

Answer:

Step-by-step explanation: