## Work Done by the Gravitational Force

The gravitational force acting on a body with mass m is equal to - mg e2. The work done by the gravity can be written as

in which (x2)2 and (x2)1 are the position of the center of mass at times t2 and t1 in the e2 direction. Gravity does positive work when the body moves downward and negative work when the body moves upward.

Equation 8.16 shows that the work done by the gravitational force on a body is independent of the path taken as the body moves from one configuration to another. In mechanics, such a force is said to be conservative. In the case of conservative forces, the work is expressible in terms of a scalar function V that is called the potential energy:

where V(t1) and V(t2) denote, respectively, the values of potential energy at times t1 and t2. Taking account of Eqn. 8.16, the potential energy Vg for gravitational force can be written as

where y is the vertical distance of the center of mass from an arbitrarily chosen datum plane. The work done by the gravitational force can be expressed as the difference in potential energy between time points t1 and t2:

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The use of dumbbells gives you a much more comprehensive strengthening effect because the workout engages your stabilizer muscles, in addition to the muscle you may be pin-pointing. Without all of the belts and artificial stabilizers of a machine, you also engage your core muscles, which are your body's natural stabilizers.

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