Activity 1: Work and work-energy theorem
In this activity, the teacher introduces the derivation of work-energy theorem using calculus as well as explaining the relationship in various methods as shown on the right. By comparing two methods of understanding work-energy theorem to each other, students will have a chance to broaden their knowledge and understanding of this topic.
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A force does work on an object and according to Newton's Second Law, the force is determined by the product of mass and acceleration of the object in motion.
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F_s = ma_s
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Uniform acceleration is average velocity over a time interval.
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F_s = ma_s = m(dv_s/dt)
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Use the chain rule.
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F_s = ma_s = m(dv_s/dt) = m(dv_s/ds)(ds/dt) = mv_s(dv_s/ds)
F_s = mv_s(dv_s/ds) |
Multiply both sides by ds and intergrate both sides.
we notie the relationship between work and kinetic energy. |
(F_s)(ds) = (mv_s)(dv_s); W = (m/2)(v_f)^2 - (m/2)(v_i)^2
W = E_k |