sph 4u unit #1 dynamics topic #2: 1d and 2d...

SPH 4U Unit #1 Dynamics Topic #2: 1D and 2D Acceleration

of 12

1.2.1 Acceleration

Some interesting statistics about top fuel dragsters::

• One Top Fuel dragster 8.2L. Hemi engine makes more horsepower than the first4 rows at the Daytona 500.

• A stock Dodge Hemi V8 isn’t powerful enough to drive the supercharger on adragster.

• Dual magnetos supply 44 amps to each spark plug (The output of an arc welder).• If spark momentarily fails early in the run, unburned nitro builds up in the affected

cylinders and then explodes with sufficient force to blow cylinder heads off theblock in pieces or split the block in half.

• In order to exceed 480 km./hr. in 4.5 seconds dragsters must accelerate at anaverage of over 4G's. In order to reach 320 km./hr. well before half-track, thelaunch acceleration approaches 8G's .

• Dragsters reach over 480 km./hr. before you have completed reading thissentence.

The Bottom Line; Assuming all the equipment is paid off, the crew worked for free, andfor once NOTHING BLOWS UP, each run costs an estimated US $1,000.00 persecond.

Putting all of this into perspective:

Imagine that you’re driving the $140,000Lingenfelter "twin-turbo" poweredCorvette Z06. Over a mile up the road, aTop Fuel dragster is staged and ready tolaunch down a quarter mile strip as youpass. You have the advantage of a flyingstart. You run the 'Vette hard up throughthe gears and blast across the startingline and past the dragster at an honest300 km.hr. The 'tree' goes green for bothof you at that moment. The dragsterlaunches and starts after you. You keepyour foot down hard, but you hear anincredibly brutal whine that sears your eardrums and within 3 seconds the dragstercatches and passes you. He beats you to the finish line, a quarter mile away fromwhere you just passed him. Think about it, from a standing start, the dragster hadspotted you 300 km.hr. and not only caught, but nearly blasted you off the road whenhe passed you within a mere 400 m. long race course. That’s ACCELERATION.


of 12

Acceleration is defined as: . There are two types ofacceleration:

1.2.1a Average Acceleration

Defined as: Calculated using:

(1.3)

1.2.1b Instantaneous Acceleration

Defined as: Calculated using:

.

Eg.#1 What is the difference between velocity and acceleration?

Eg.#2 A track runner starting from rest, reaches a velocity of 9.3m/s [fwd] in 3.9 s.Determine the runner’s average acceleration.

Eg.#3 The Renault Espace F-1 is a modifiedproduction car that can go from rest to 100. km/hrwith an average acceleration of 9.52m/s [fwd]. How2

long does it take the Espace F-1 to achieve its finalspeed of 100. km/hr?


of 12

Eg.#4 After hitting the target, an arrow undergoesan average acceleration of 1.37×10 m/s [W] in3 2

3.12×10 s, then stops. Determine the initial velocity–2

of the arrow when it hit the target.

1.2.2 Graphing Accelerated Motion

Eg.#5 A graph of position vs. time of a dynamics cart is shown below:


of 12

Time (s) ( )

0

2.0

4.0

6.0

8.0

a) Draw a smooth curve through the data points, use it to calculate the slopes of thecurve at each data point and record in the table below:

b) What does the slope represent?

c) Graph the data in the table above onto the graph paper below and join the datapoints with a straight line.


of 12

Time (s.) Area ( )

0

3.0

6.0

9.0

d) Calculate the slope of the straight line. e) What does this slope represent?

Eg.#6 The acceleration vs time graph of the motion of a car initially at rest is shown:

a) Find the area of the 3 rectangles inthe graph above and record in the table:

b) What do the areas represent?


of 12

Time (s.) ( )

3.0

6.0

9.0

c) Draw the associated velocity – time graph below (remember, the car was initially atrest):

d) Calculate the total area under the graph at each of the times in the table below:

e) What are the dimensions of the area?

f) What do these quantities represent?


of 12

1.2.3 Graphing Accelerated Motion – Summary

Eg.#7 Complete the table below:

Type of graph Area Under Slope of a Tangent Line Slope of a Secant Line

position vs time

velocity vs time

acceleration vs time

Eg.#8 Describe the motion depicted in each graph below:

a) b)

c) d)


of 12

1.2.4 Solving Constant Acceleration Problems

So far, we’ve used the equation to solve problems. Sometimes however

we are not given all of these quantities. We need other kinematics equations.

Formula Variables Involved Variables Missing

(1.2)

(1.3)

(1.4)

(1.5)

Eg.#9 A ball rolls down a hill, starting from rest, with an acceleration of 1.0 m/s [down2

the hill].

a) What is the velocity of the b) How far did the ball travel after 9.0ball after 7.0 seconds? seconds?


of 12

1.2.5 Acceleration in Two Dimensions

We saw earlier that . This equation also applies in 2 dimensional situations.

The catch is that is a vector subtraction.

Eg.#10 Calculate the acceleration of a car that travels initially at 80. km/hr [N] and afteraccelerating for 2.5 seconds is now traveling at 100. km/hr [N30°E]


of 12

Worksheet 1.2

1. What condition must be true so that instantaneous acceleration and averageacceleration are equal?

2. An aircraft while preparing to land changes its velocity from 1650km./hr.[W] to 1120km./hr.[W] in a time of 345 seconds. Calculate the average acceleration of the aircraftin

a) (km./hr.)/s. b) m./s.2

3. Sketch a graph of a car that has increasing speed and decreasing accelerationduring a time of 4.0 seconds.

4. Describe the motion depicted by each graph shown below:

a)


of 12

b)

c)

5. A car, initially travelling at 26m./s.[E] slows down with a constant averageacceleration of 5.5m./s. [W]. Determine its velocity after 2.5 seconds.2

6. A bullet, starting from rest exits the 0.56m. long barrel of a gun, after acceleratingalong its length with a velocity of 420. m./s.[fwd].

a) What is the average velocity of the bullet in the barrel?


of 12

b) What is the average acceleration of the c) How long does it take the bullet to bullet in the barrel? travel the length of the barrel?

7. A car (C) ad a van (V) are stopped besideone another at a red light. When the lightturns green, the motion of each vehicle is asshown in the graph below:

a) After the light turns green, when do bothvehicles have the same velocity?

b) After the light turns green, when does the vanovertake the car? Answers:

2a)

b)

5)

6a)

b)

c)

7a)

b)

sph 4u unit #1 dynamics topic #2: 1d and 2d...

Documents