Question

A force F = x² + 2y acts on a body
and displace it from (1,2) to (3,4)
Find the work done.​
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Answer 1

Given :

A force F = x² + 2y acts on a body and displace it from (1,2) to (3,4).

To Find :

Work done by the force.

Solution :

■ Work done is measured as the product of force and displacement.

• W = F d
• It is a scalar quantity having only magnitude.
• SI unit : J (joule)

Since force is variable in this case we have to integrate force equation wrt displacement.

Let's solve it :)

➠ $\sf\:dW=F\:ds$

➠ $\sf\:dW=(x^2+2y)\:dx\:dy$

➠ $\displaystyle\sf\:W=\int dW=\int (x^2\:dx)+(2y\:dy)$

➠ $\sf\:W=\bigg[\dfrac{x^3}{3}\bigg]_1^3+\bigg[\dfrac{2y^2}{2}\bigg]_2^4$

➠ $\sf\:W=\bigg[\dfrac{(3)^3-(1)^3}{3}\bigg]+\Big[(4)^2-(2)^2\Big]$

➠ $\sf\:W=\bigg[\dfrac{27-1}{3}\bigg]+(16-4)$

➠ $\sf\:W=\dfrac{26}{3}+12$

➠ $\sf\:W=8.67+12$

➠ $\underline{\boxed{\bf{\orange{W=20.67\:J}}}}$

Answer 2

Answer:

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