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Physics: Problems and Solutions

Force

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Force is an influence on an object that causes it to accelerate. Its units are given in kg·m/s2, or Newtons (N). Force is given by the formula

\vec{F} = m \vec{a}

Average force is equal to a change in linear momentum over time for a given interval, and instantaneous force is equal to the derivative of linear momentum with respect to time.

p_\mathrm{avg} = \frac{\Delta F}{\Delta t}\,
p = \lim _{\Delta t\rightarrow 0} \frac{\Delta F}{\Delta t} =  \frac{\mathrm{d}F}{\mathrm{d}t}\,

If force is variable and given as a function \vec{F} = f(x) (with x being the position), and b - a is the interval over which the force acts, work is given by

W = \int^b_a f(x)dx

If the force is constant, this simplifies to

W = \vec{F} d

Some common forces include the force of gravity, the normal force, and the force of friction.

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