LAB 3: BALL PHYSICSCS 282

Questions about Assignment 1?

Questions about last week’s lab?

Otherwise, please sit next to your partner (or someone else if your partner isn’t here)!

Housekeeping…

We are going to make a ball fall and bounce off a table… with physics!

In a nutshell,◦ Get a ball to fall in the framework◦ Collision checking◦ Changing velocity◦ Energy Relationships

And for the over achievers…◦ Realistic animation

What’s the plan for today?

First of all, download the framework for today’s lab ( Resources in class website)

Take a look at the framework. Namely◦ The body class (body.h and body.cpp)◦ lab3.cpp (the driver)

Notice that the body class has◦ 3 vectors: position, velocity, acceleration◦ 2 scalars: mass, energy

So now let’s make the ball fall!

Framework

How do you update the position of the ball?◦ For now, we are going to assume the ball can only

move in the y-direction, so ignore x and z.◦ If you know the velocity and the delta time, you

can update the position!

How do we get delta time?◦ Since we have a clock class, and a clock called

“delta_time” in our driver, all we need to do is call the measure_reset() function We use measure_reset because delta time should be

reset after its value is read.

Exercise 1: Falling Ball (Integration)

Go into body.cpp◦ Edit the “update_position” function

Add the C++ equivalent of:y_position = y_position + ( y_velocity * delta_t )

Go into lab3.cpp◦ Notice the variable “sphere” and its parameters

For this exercise, we let the sphere have an initial velocity of -2.0

◦ Look at the DrawGLScene() function Notice the part commented “Sphere Physics” Under “Sphere Physics” use the global_time object and

update_position function to correctly update sphere’s postion.

Exercise 1

Our ball fell magnificently!◦ But it also fell through the table…

Since we never check for a collision between the ball and the table, there is no interaction between them

We need to fix that!

Success!.... Wait, what?!

Things to consider when doing collision◦ The position of your object (in this case, the ball)◦ It’s size ( radius for us )◦ The position of the object we want to check

You want to make the ball stop when it hits the table.◦ The table is situated at ( 0.0, -0.5, 0.0)◦ The radius of the ball is 0.5◦ Conveniently, this allows us to just check the

collision at 0.0 Go into body.cpp

◦ Modify the update_position function The ball should stop when it touches the table

Exercise 2a: Collision Checking

Our ball now stops at the table…◦ But something is still wrong

The ball is falling at constant speed – which would be OK if there was no acceleration.◦ Unfortunately for us, we have gravity

Exercise 2b: Velocity

So we need to update our velocity based on acceleration

Acceleration due to gravity is -9.81 m/s2

Examine the your change to update_position◦ It should be testing for y_position >=0

Add this same check to update_velocity◦ Inside the check, add the C++ equivalent of:

y_velocity = y_velocity + (delta_t * gravity) This should be the only statement inside of this check

right now.

At this point, our ball will accelerate until it touches the table.

Exercise 2b: Velocity

But something is still missing…

Great! We have an accelerating, colliding ball now!

Please switch drivers!

Next we will make the ball bounce. For now, we will just switch the sign of the y

velocity once the ball has hit the ground Go to body.cpp

◦ In update_velocity, add a check to switch the velocity sign. In other words: If y_position < 0, switch y_velocity signs

The ball now bounces up and down!

Exercise 3: Bouncing

We are still missing one more thing – when the ball hits the ground, it should not bounce up to the same height.

The ball starts off with a certain amount of potential energy. When it hits the ground, this energy is converted to both kinetic and thermal energy.

Thus we our ball will have a lower kinetic energy, and will not bounce as high!

Energy

First, you need to figure out the initial potential energy of the ball.◦ Ep = m*g*h

mass * 9.81 * height of the ball◦ Go to body.cpp, and calculate energy in the

constructor (since we know all our parameters at that point already!)

Next, we need to remove some things◦ Remove the if statement in update_position◦ Remove the if-else in update_velocity

Exercise 4: Implementing Energy

At this point, your update_velocity and update_position functions should have 1 line of code.

We need to know, however, when the ball has hit the table (or gone underneath it)◦ Before you change the y-position in

update_position, add a check for this and manually set the y-position to 0 (I’ll explain why we do this later).

Inside this check you’ve added, we can know calculate energy and our new velocity!

Exercise 4

To account for thermal energy, reduce the ball’s energy by 20%◦ energy *= 0.8

You have your energy and mass, therefore you can solve this equation for velocity◦ Ek = ½ m*v2

Math time! Solve the equation for v to get the equation you need.

◦ Now set your y-velocity to this new velocity Congratulations! You have successfully

implemented a (quasi) realistic bouncing ball!

Exercise 4

Manually setting the position of the ball to 0 is an incorrect way of animating what’s really occurring. The correct way is to detect the instant the ball hits the table, and subtract that from your recorded delta time.◦ animation_t = delta_t – collision_t

Then, you can animate the ball bouncing up for this amount of time, and this will be the “realistic” way of animating your ball.

Sidenotes

Questions?