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10 February 2005

Dear Recipient, You are privileged to obtain a partial collection of answers for MEG 207 Dynamics. This document was compiled from PDF files collected during Fall of 2002 and Spring 2003. I have complied them into one document with Bookmarks to aid you in quickly finding the solutions you need. Unfortunately this isn’t a complete compilation of all of the answers, butcomprehensive enough to help complement your studies. Engineering Mechanics, Dynamics, Second Edition. ISBN: 0-471-05339-2

Happy Studies!

Chapter 13

Chapter 14

Chapter 15

Chapter 16

Chapter 17 Old Exams

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UNLV, DEPARTMENT OF MECHANICAL ENGINEERING MEG 207, SPRING 2002, FIRST TEST Closed Book, one page of handwritten notes allowed. Enter the answer for each question into the space provided. Enter SI units in all answer spaces with brackets ( ). 1. (15 points) A vehicle traveling at 108 km/h suddenly decelerates at a rate of3 m/s . a) Determine the time needed for the vehicle to come to rest. b) Determine the distance traveled between the beginning of braking, and the full stop.
1(a) v0 := 108⋅ in m/s a := −3 3600 v ( t) v0 + a⋅ t General equation. Solving for t when v=0 v0 gives: t := and t = 10 −a 1 2 2 1 (b) v*dv = a*dx or a⋅ distance ⋅ ( 0 − v0) −v0 distance := distance = 150 2 2⋅ a 1000
2

Answers: a) b)Tstop = dStop =

10 150

(

s

units) units)

( m

2. (20 points) A ball of mass m is thrown horizontally from a bridge 30 m above ground. It touches ground at distance d = 15 m. Determine the ball's initial velocity. No friction.

v0
A (x0,y0)
y

g

h = 30 m x

horiz. distance d = 15 m

B

Problem 2 d := 15 h := 30 Angle is zero. Horizontal: d = v0*t. Vertical: y(t) =y0 -1/2*g*t^2. At point B, y = 0. Given d v0⋅ t 0 h − 0.5⋅ g ⋅ t
2

g := 9.81

res := Find( t , v0)

res = 

 2.473    6.065 
( m/s )

v0 =

6.065

1

P y
R=2 m

θ

x

3. (20 points) Pin P moves at constant speed of 3 m/s in a counterclockwise sense around the circular slot with radius r = 2 m. Determine (a) the angular velocity of P. (b) the totalacceleration vector ( Use polar coordinates: er and eθ directions) of pin P when θ = 30 degrees. (c) the magnitude and angle of the resultant acceleration vector in Cartesian x-y coordinates. (b) no radial or angular accel. In neg. er direction we 2 2 have r*ω = - 2*2.25 m/s (c) Resultant Acceleration is purely inward, thus: o o ax = -4.5*cos 30 and ay = -4.5*sin 30

4.5 Answer ω = aP = aP = v/r = 3/2 =1.5 -4.5
2

( rad/s er 0 eθ (m/s )
2

)

4.5 m/s at -150 degrees
20 0
Rai n

(magnitude and angle in x-y coordinates) 4. (25 points) Wind-driven rain is falling 0 with a speed of 30 m/s at an angle of 20 to the vertical as shown at left. Determine the angle ψ at which the rain is seen by passengers inside the bus. The bus is traveling at 72 km/h. Vrain = VBus + VRain/bus Vbus = 20m/sψ
y

v = 72 km/h

x-and y-components of VRain/bus: v R/B,x = -Vbu -- VR*sin(20deg) = -30.2 m/s v R/B,y =-- VR*cos(20deg) = -28.19 m/s = tan (29.19/30.2) = 43 deg.
-1

VRain/bus
ψ

Angle ψ seen by moving passengers =

43 deg.

(

)

2

5. (20 points) In the pulley system shown at left, the cable is attached at C. Mass B moves to the left at vB = 3 m/s, and accelerates y 2 Balso to the left at aB = 0.5 m/s . Using the x-y x C frame with origin at C, determine: (a) the velocity of A (b) the acceleration of A

A
Differentiation gives: 2 vB = vA and 2 aB = aA

L = 2xB(t) +(Y0 -- yA(t)) -

6 m/s 1 m/s
2

(

)

aA =

(

)

3

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UNLV, DEPARTMENT OF MECHANICAL ENGINEERING MEG 207, Spring 2002,...