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# lec06 - Impulses 1 2.003J/1.053J Dynamics and Control I...

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Cite as: Thomas Peacock and Nicolas Hadjiconstantinou, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 1 Impulses 2.003J/1.053J Dynamics and Control I, Spring 2007 Professor Thomas Peacock 2/26/2007 Lecture 6 Collisions Impulses Large forces acting over a short period of time Impulsive forces result in an instantaneous change of velocity (linear momen - tum) Newton’s 2nd Law Application: t 2 fdt = p p = mv 2 mv 1 2 1 t 1 For an impulsive force: f = Δ ( t ) 0 + δ ( t ) dt = 1 0 Figure 1: Impulsive force. In a time versus force graph, this is shown by a sharp spike with finite area. Figure by MIT OCW. Impulse occurring between t = 0 and t = 0 + :

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Cite as: Thomas Peacock and Nicolas Hadjiconstantinou, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. Collisions in a 1-D System 2 t =0 + Δ p Δ ( t ) dt = Δ p = m [ v (0 + ) v (0 )] v (0 + ) v (0 ) = t =0 m Therefore, impulse response is just the natural free response for the initial con - dition: Δ p v (0) = m Key Points All other forces (e.g. gravity, dashpot damping) are considered negligible during impact. As the time interval shrinks, the effect of these finite forces becomes negligible. By direct analogy, for rotational systems one can have torques of an impulsive nature. The impulsive torque changes the angular momentum. τ = Δ ( t ) t =0 + Δ ( t ) dt = Δ H where Δ H is the change in angular momentum of the system. t =0 Collisions in a 1-D System Before: Figure 2: Two balls traveling with v 1 > v 2 . Figure by MIT OCW.
Cite as: Thomas Peacock and Nicolas Hadjiconstantinou, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology.

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lec06 - Impulses 1 2.003J/1.053J Dynamics and Control I...

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