Study problems for L1a – rectilinear kinematics: continuous motionlearnline.cdu.edu.au/lecturers/gheins/ENG152/Tutorials/... · 2010-07-09 · ENG152 Dynamics Study Guide L1 9 Study

ENG152 Dynamics Study Guide L1 1

Study problems for L1a – rectilinear kinematics: continuous motion

(Hibbeler sections 12.1-12.2)

Workbook problem (“How did they get those answers?”)


Solution to Workbook problem


Study problems

When you can, it’s usually quicker to use the equations for constant acceleration (Equations 12.4 to

12.6), but first you have to work out if they apply. If they don’t, then you use Equations 12.1 to 12.3

plus calculus.

Both study problems are “continuous motion”, but how would you know this if you weren’t told?

12.1 (Hibbeler 11 ed.) 12.13 (Hibbeler 11 ed.)

Question A truck, travelling along a straight

road at 20km/hr, increases its speed

to120km/hr in 15s. If its

acceleration is constant, determine

the distance travelled.

The velocity of a particle travelling

in a straight line is given by v = (6t -

3t2) m/s, where t is in seconds. If s

= 0 when t = 0, determine the

particle’s deceleration and position

when t = 3s. How far has the

particle travelled during the 3s time

interval, and what is the average

speed?

MAKE SURE THAT YOU HAVE A GO AT THE QUESTIONS BEFORE YOU HAVE A LOOK AT THE HINTS BELOW

General Hints Is the acceleration constant? It’s a give-away

in this question.

Is acceleration constant? Look at the equation

you get for a.

Specific Hints It’s all straightforward once you’ve decided

if a=const.

Finding total distance travelled can be tricky –

it’s not the same as displacement. Ex 12.5

gives clues and explains why the instant at

which v=0 is important. Drawing a diagram

can help. Average speed is explained in

Section 12.2.

Answer d = 291.7m a = -12m/s2;

s = 0;

sT = 8m;

average speed = 2.67m/s


Study problems for L1b – rectilinear kinematics: erratic motion (Hibbeler sections 12.3)





Study problems

How would you know these were “erratic motion” if the lecture heading didn’t tell you?

In these questions you’ll interpret graphs using equations 12.1 to 12.3. You’ll have to work out which

ones you want – 12.3 usually goes with graphs where s is plotted along the abscissa (horizontal axis).

Examples 12.6, 12.7, 12.8 are good.


Question A car travels along a straight road

with the speed shown by the v-t

graph. Determine the total distance

the car travels until it stops when

t=48s. Also plot the s-t and a-t

graphs.

The v-s graph was determined

experimentally to describe the

straight line motion of a rocket sled.

Determine the acceleration of the

sled when s=100m and when

s=200m.


General

Hints

What is plotted on the abscissa (“x axis”)? The

first part is quick once you know how.

Sketching the curves takes longer – you’ll use

two of the equations mentioned on the previous

page.

Check the abscissa. So which equation will

you use? Once you’ve got the right one it’s

straight forward. (Is acceleration constant?)

Specific

Hints

One of the examples in Hibbeler is very similar.

One of the examples in Hibbeler should be

very helpful

You’ll need to get the gradient and interpolated

values from the graph to use in the equation

you’ve selected.

Answer s = 144m At s=100m, a=4.48m/s2

At s=200m, a=7.04m/s2


Study problems for L1c – curvilinear motion: rectangular coordinates (Hibbeler sections 12.4-12.5)





Study problem

This problem is a direct application of principles – no tricks.

12.67 (Hibbeler 11 ed.)

Question The velocity of a particle is given

by v = {16t2i + 4t

3j + (5t+2)k} m/s,

where t is in seconds. If the

particle is at the origin when t=0,

determine the magnitude of the

particle’s acceleration when t=2s.

Also what is the x,y,z coordinate

position of the particle at this

instant?


General Hints Examples 12.9 and 12.10 are the ones to

review, and the “Procedure for Analysis” on

p35 of Hibbeler is good.

Specific Hints You’ll use the ideas of Sections 12.4 and

12.5 – especially 12.5. These rectangular

components are like three separate rectilinear

motions happening at the same time, so

you’ll be using the work in Lecture L1a as

well.

Answer a=80.2m/s2

(42.7m, 16.0m, 14.0m)


Study problems for L1d – projectile motion (Hibbeler sections 12.6)





Study problems

Projectile motion is a classic application of rectangular components. Follow the Procedure for

Analysis in Section 12.6 – see Examples 12.11 – 13.

Finding the theoretical maximum range is a common projectile question. Why might the maximum

range be different in practical applications?


Question Show that if a projectile is fired

at an angle θ from the

horizontal with an initial

velocity v0, the maximum range

the projectile can travel is given

by Rmax = v02/g, where g is the

acceleration of gravity. What is

the angle θ for this condition?

The snowmobile is travelling at 10m/s

when it leaves the embankment at A.

Determine the time of flight from A to B

and the range R of the trajectory.


General Hints Standard procedure can be used here.

This is made tricky by the sloping hill. Example

12.13 is a good start.

Specific Hints Write down expressions for the x and y-

components of the particle’s initial

speed and use the equations of projectile

motion to find the distance travelled by

the particle in each direction. Set y = 0

to determine the range and eliminate t

(it’s the same for both directions).

Apply equations for projectile motion from A to B.

This time you can’t set a fixed figure for y at impact

so you’ll need to relate the drop height from A to B

to the range R. It works out quite neatly in the end

Answer Θ=45 deg. t = 2.48sec, R = 19.02m

Documents

Study problems for L1a – rectilinear kinematics: continuous motionlearnline.cdu.edu.au/lecturers/gheins/ENG152/Tutorials/... · 2010-07-09 · ENG152 Dynamics Study Guide L1 9 Study