Work Done by a Variable Force (Leaving Cert Applied Maths): Quizzes

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Work Done by a Variable Force
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What formula calculates work done by a constant force?

W=FdW = Fd

Why is integration needed for variable force work?

Force changes continuously

What is the formula for work by a variable force from position AA to BB?

W=∫ABF(x)dxW = \int_A^B F(x)dx

In W=∫ABF(x)dxW = \int_A^B F(x)dx, what does F(x)F(x) represent?

Force as function of distance xx

How does force vary with extension for elastic strings following Hooke's Law?

Increases linearly

For k=14k=14 N/m, l0=0.5l_0=0.5 m, what is FF when xx is total length (Method 1)?

F=14x−7F = 14x - 7

For k=14k=14 N/m, what is FF when xx represents extension only (Method 2)?

F=14xF = 14x

Work to stretch string from natural length 50 cm to 1.5 m (extension 0 to 1 m)?

7 J

Work to stretch string further from 1.5 m to 2.5 m (extension 1 m to 2 m)?

21 J

What equals the total work done stretching from natural length for elastic systems?

Potential energy gained

What must match your chosen variable definition in variable force problems?

Integration limits

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