# n7_4 - Section 7.4 Work courtesy Chia-Rong Chen 1 When a...

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Unformatted text preview: Section 7.4 Work courtesy: Chia-Rong Chen 1. When a constant force F acts on an object in the same direction as the displacement d , the work done by the force is W = Fd (units: joule [J] = newton-meter; or, ft-lb) 2. For a body moves along the x-axis from x = a to x = b under a varying force F ( x ), we divide [ a, b ] into sub- intervals of length Δ x i and approximate the force in the subinterval by F ( x ∗ i ) with x ∗ i ∈ [ x i − 1 , x i ]. Then the work done over the subinterval is W i ≈ F ( x ∗ i ) Δ x i The total work done over the interval [ a, b ] is thus the limit of the Riemann sums, W = lim bardbl P bardbl→ n summationdisplay i =1 F ( x ∗ i )Δ x i = integraldisplay b a F ( x ) dx eg.(1) A point is moved along the x-axis from x = 3 m to x = 6 m by a force that measures F = 2 x 2 + 1 N. Find the work done. 3. Hooke’s law states that the force F required to stretch or compress a spring x units from its natural length is F = kx, where k = spring constant eg.(2) A spring of natural length of 1 m stretches to 1.8 m under a 24 N force. How much workeg....
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n7_4 - Section 7.4 Work courtesy Chia-Rong Chen 1 When a...

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