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 is the formula for work done by a constant force?

W=FdW = Fd

Why do variable force problems require calculus rather than basic algebra?

Force changes continuously

What is the formula for work done by a variable force?

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

What law do elastic strings follow?

Hooke's Law

When using Method 2 for elastic strings, what does xx represent in F=kxF = kx?

Extension only

What result do both methods give when applied correctly to elastic string problems?

Identical results

For k=14k = 14 N/m, l0=50l_0 = 50 cm, what work stretches from 50 cm to 1.5 m?

7J

What additional work stretches the string from 1.5 m to 2.5 m?

21J

What equals the total work done in stretching from natural length?

Potential energy gained

Does the choice of reference point affect the final answer?

No

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