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The work W done by the net force on a particle equals the change in the particle’s kinetic energy KE: \(\mathrm{W=ΔKE=\frac{1}{2}mv_f^2−\frac{1}{2}mv_i^2}\). The work-energy theorem can be derived from Newton’s second law.
- 7.2: Kinetic Energy and the Work-Energy Theorem
The work-energy theorem states that the net work \(W_{net}...
- 7.2: Kinetic Energy and the Work-Energy Theorem
The work-energy theorem states that the net work \(W_{net} \) on a system changes its kinetic energy, \(W_{net} = \frac{1}{2}mv^2 - \frac{1}{2}mv_0^2\).
Work-Energy Theorem argues the net work done on a particle equals the change in the particle’s kinetic energy. According to this theorem, when an object slows down, its final kinetic energy is …
net =m(v)dv v i v f ∫and the integral of this equation is: ⇒W net =m v2 2 ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ v i v f Read: The net work equals the mass of the object times the velocity of the object squared divided by two from velocity initial to velocity final. Which works out to be: ⇒W net = 1 2 mv f 2− 1 2 mv i 2 This is where the definition of ...
The work-energy theorem states that the work done on an object by the net force acting on it is equal to the change in its kinetic energy. In other words, the work done on an object transfers energy to or from it, resulting in a change in its kinetic energy.
The measurement of work and energy with the same unit reinforces the idea that work and energy are related and can be converted into one another. 1.0 J = 1.0 N∙m, the units of force multiplied by distance. 1.0 N = 1.0 kg∙m/s 2, so 1.0 J = 1.0 kg∙m 2 /s 2.
According to this theorem, when an object slows down, its final kinetic energy is less than its initial kinetic energy, the change in its kinetic energy is negative, and so is the net work done on it. If an object speeds up, the net work done on it is positive. When calculating the net work, you must include all the forces that act on an object.
