PHYS 1151 Study Guide - Final Guide: Elastic Modulus, Scilab, Damping Ratio

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grayhippopotamus677

6 Sep 2018

School

Northeastern University

Department

Physics

Course

PHYS 1151

Professor

Matthew Webber

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Document Summary

The basic units are time, length, mass, and number of # (particles/objects/etc. ) T t n e m e c a p s. Derivative of the position (displacement) vs. time gives velocity: ! Tf ti vtd t = x d x d t. X = v t d v d t d 2x d 2t a(t)d t. V = vf vi = tf ti. Acceleration is ! a = v vo t. Displacement of a motion with acceleration is ! a t 2. X = vot + v2 v2 o v vo. X is either at rest or at a motion with. If an object does not have any acceleration, then it constant velocity, ! v = 0 or ! v = con st. , and the force applied to this object is equal to. If the body moves with some acceleration, it experiences a of force is !

Related Questions

A string of length 3 m and total mass 12 g is under a tension of 160 N. A transverse harmonic wave with wavelength 25 cm and amplitude 2 cm travels to the right along the string. It is observed that the displacement at x = 0 at t = 0 is 0:87 cm.
(i) What is the speed of the wave?
(ii) Write the wave function, y(x; t).
(iii) Find the particle velocity at position x = 0 at time t = 10 s. What is the maximum particle velocity?

kalanji71199

A particle of mass m moves under the influence of a central force.The potential energy function is
V(r) = {
K (a2âr2) /2 if r â¤ a
0 if r > a

as illustrated in the figure. The initial position is (x,y) = (a/2,0) and the initial velocity is (vx,vy) = (0, v0).
[Data: m = 1.0 kg; K =17.1 N/m; a = 1.0 m; r0 = 0.5 a; v0 = 2.0m/s.]

(A) Determine the time ta when the mass crosses the boundary r =a.

(B) Determine angular position Ïa where the particle crosses theboundary r = a.

***HINT GIVEN***

Use the constants of the motion to analyze the orbit.

Write L = mr^2 dÏ/dt = the initial value.
What is the initial value?

Write E = (1/2)m (dr/dt)^2 + L^2/(2mr2) +V(r )
= the initial value. What is the
initial value?

Part A. In the energy equation,
change the variable from r to u,
where r =sqrt(u). The result can be
solved by u(t) = c1+c2 cosh(Î±t).
Determine c1, c2, and Î±.

Part B.
Ï = Integral 0 to t [L/(mr^2)] dt

The position of a particlemoving along the x axis depends on thetime according to theequation x=ct²- bt³,where x is in meter antt in seconds. what are the units of (a)constant c and (b) constant b? Let their numerical values be 3.0and 2.0,respectively. (c) At what time does the particle reach itmaximumpositive x position? From t= 0.0s to t= 4.0s, (d) whatdistancedoes the particle move and (e) what is its displacement?find itsvelocity at times (f) 1.0s, (g) 2.0s, (h)3.0s, and (i)4.0s. Findits acceleration at times (j) 1.0s, (k) 2.0s, (l) 3.0sand (m)4.0s.

PHYS 1151 Study Guide - Final Guide: Elastic Modulus, Scilab, Damping Ratio

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