[M2-MAIN] Rectilinear Motion PDF

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Summary

a linear motion in which the direction of the velocity remains constant and the path is a straight line....

Description

19/06/2020

Dynamics of Rigid Bodies

Module 2

Rectilinear Motion of Particles

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Define the following: 1. Position 2. Velocity 3. Acceleration

P

Position

V

Velocity

A

Acceleration

Particles have mass but negligible size and have only 3 translational degrees of freedom. Kinematics of particles with 1 DOF. This is called rectilinear motion.

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The basic equations Almost every particle rectilinear kinematic problem can be solved by manipulating the following three equations.

Velocity: v = ds/dt Acceleration: a = dv/dt Acceleration as a function of position: a ds = v dv

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Time-dependent equations

If the velocity or acceleration are dependent on time, the above velocity and acceleration equations may be integrated to find position or velocity. Note that when integrating, limits are required to obtain a solution. Velocity → Position: v = ds/dt → ∫v dt = ∫ds Acceleration → Velocity: a = dv/dt → ∫a dt = ∫dv

Position-dependent equations If the velocity or acceleration are dependent on position, the following equation may be used.

Acceleration depends on position: ∫a ds = ∫v dv Velocity depends on position: ∫dt = ∫(1/v)ds

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Acceleration as a function of velocity

If the acceleration depends on velocity, the following equations may be used. Acceleration → Velocity: ∫dt = ∫(1/a) dv Acceleration → Position: ∫ds = ∫(v/a) dv

Constant-acceleration equations If acceleration is constant, the following equations may be used.

v = v0 + a0(t - t0) v2 = 2a0(s - s0) + v02 s = s0 + v0(t - t0) + a0(t - t0)2/2

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1.

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Reference F.B. Beer, E.R. Johnston, D.F. Mazurek, P.J. Cornwell, E.R. Eisenberg (2009): Vector Mechanics for Engineers (9t Edition), McGraw Hill, New York. Richard Hill and Kirstie Plantenberg (2013): Conceptual Dynamics - An Interactive Text and Workbook, SDC Publications, Kansas. F.B. Beer, E.R. Johnston, D.F. Mazurek, P.J. Cornwell (2016): Vector Mechanics for Engineers (11t Edition), McGraw Hill, New York.

よく勉強し、必要に応じて尋ねてください

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Module 2

Rectilinear Motion of Particles

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Add them together (ignore the sign since distance is asked…!!!

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It has 2 roots: but get only the positive value

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Reference F.B. Beer, E.R. Johnston, D.F. Mazurek, P.J. Cornwell, E.R. Eisenberg (2009): Vector Mechanics for Engineers (9t Edition), McGraw Hill, New York. Richard Hill and Kirstie Plantenberg (2013): Conceptual Dynamics - An Interactive Text and Workbook, SDC Publications, Kansas.

よく勉強し、必要に応じて尋ねてください

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