A block of mass m is pulled by a force F = ( 3 x 2 + 2 x ) i ^ N along the x-axis. If the block moves from x = 1 m to x = 3 m, the work done by this force is:

The work done by a variable force is given by W = ∫ F ⋅ d r . Here, F = ( 3 x 2 + 2 x ) i ^ and d r = d x i ^ . W = ∫ 1 3 ( 3 x 2 + 2 x ) d x = [ x 3 + x 2 ] 1 3 W = ( 3 3 + 3 2 ) − ( 1 3 + 1 2 ) = ( 27 + 9 ) − ( 1 + 1 ) = 36 − 2 = 34 J

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PhysicsW.E.P.Calculation of workMedium2 minai-gemini

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A block of mass $m$ is pulled by a force $F = (3 x^{2} + 2 x) \hat{i}$ N along the x-axis. If the block moves from $x = 1$ m to $x = 3$ m, the work done by this force is:

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Answer:

Solution:

The work done by a variable force is given by $W = \int F \cdot d r$ .

Here, $F = (3 x^{2} + 2 x) \hat{i}$ and $d r = d x \hat{i}$ .

$W = \int_{1}^{3} (3 x^{2} + 2 x) d x = [x^{3} + x^{2}]_{1}^{3}$

$W = (3^{3} + 3^{2}) - (1^{3} + 1^{2}) = (27 + 9) - (1 + 1) = 36 - 2 = 34 J$

Stream:JEESubject:PhysicsTopic:W.E.P.Subtopic:Calculation of work

⏱ 2mℹ️ Source: ai-gemini

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