Impulse: Difference between revisions

Revision as of 23:19, 19 January 2010

Definition

The impulse due to a force applied over a period of time is the integral of the force over the period of time. In other words, the impulse due to a force ${\overline {F}}(t)$ (a vector quantity) from time $t=t_{1}$ to time $t=t_{2}$ is given by

$\int _{t_{1}}^{t_{2}}{\overline {F}}(t)\,dt$

Impulse is responsible for a change in the linear momentum, and the net impulse on a system equals, as a vector, the change in the linear momentum of the system. This is one of the many formulations of Newton's second law.

The concept of impulse is particularly useful for collisions, where a very large and quickly changing quantity of force is exerted by the two bodies on each other over a very short interval of time. Measuring the force as a function of time is hard, but the total value of the impulse can both be measured and theoretically predicted.

Units and dimensions

The $MLT$ dimensions of impulse are $MLT^{-1}$ , and the SI units are $kgm/s$ (kilogram meters per second).

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 ==Definition==
-The '''impulse''' due to a force applied over a period of time is the integral of the force over the period of time. In other words, the impulse due to a force <math>F(t)</math> from time <math>t = t_1</math> to time <math>t = t_2</math> is given by
+The '''impulse''' due to a force applied over a period of time is the integral of the force over the period of time. In other words, the impulse due to a force <math>\overline{F}(t)</math> (a vector quantity) from time <math>t = t_1</math> to time <math>t = t_2</math> is given by
-<math>\int_{t_1}^{t_2} F(t) \, dt</math>
+<math>\int_{t_1}^{t_2} \overline{F}(t) \, dt</math>
 Impulse is responsible for a change in the [[linear momentum]], and the net impulse on a system equals, as a vector, the change in the linear momentum of the system. This is one of the many formulations of [[Newton's second law]].