Roller coaster physiks 3

Warm up exercises

A battleship simultaneously fires two shells at enemy ships. If the shells follow the parabolic trajectories shown, which ship gets hit first?

1) A

2) Both at the same time

3. B

4.) Need more information.

It depends only on the high of the trajectory to decide which ship gets hit first

From postion vs. time graph to acceleration vs. time graph.

Position graph. Position vs. Time

Parabolic graph

v = delta x / delta t -> dx / dt = slope of x vs. t graph.

The slope of this graph is the velocity.

v vs. time

Linear graph

Acceleration

Constant graph.

Now we are going in the other direction:

(Integrating the area below the a vs. t graph)

Starting with the acceleration graph.

With our roller coaster measurement:

For some reasons we somewhere know the velocity.

At some time t₀ we know the velocity v₀ somehow.

Question: what is the speed at some other time?

What would be a way to approximate the speed?

If the acceleration would be constant, we could multiply the acceleration by the time.

If we take this average acceleration we can do this calculation.

We do calculate the area of a rectangle.

This is only an approximation. How could we improve this?

We could make smaller rectangles.

Can you see what this is? This is calculus.

Let the numbers of rectangle go to infinity.

We are computing the area under the curve: A fancy word: integration.

A fancy word for getting the slope: derivative.

Speeding up is reflected in the fact, that the area here is positive.

(Areas under the x-axis count negative.)

Break

Introduction to logger pro

An example of Millennium Force

How to get the total of three vectors, the magnitude?

You can use Pythagoras. (Since the vectors are perpendicular)

Interpretation of data’s from logger pro:

It seams that the high only takes certain values. This is not a problem or noise, but a problem of the internal function of the barometer.

The barometer first produces an analog signal, but this is converted into a digital signal. This digital signal can only have some discrete values, and this is what we see here.

How could you find your change in position?

It’s the same as going from average acceleration to speed;
we go from average velocity to displacement.

Delta x = Sum(i=1 to N of v(t_i) multiplied by delta t)

If acceleration is not constant, as it should be on a roller coaster, then the force cannot be constant.

So we need to know more about Newton’s laws.

Newton’s first Law

Question: A car rounds a curve while maintaining a constant speed.
Is there a net force on the car as it rounds the curve?

There is a force.

Which way does this force point?

Experiment Pizza:

Three cups, filled with water (and glued to the table), on top a pizza-pan, on top three cups with three balls.

Pulling on the pizza-pan will pull away the three cups and the balls will fly straight down into the three cups, filled with water.
(The same experiment as with the tablecloth)

Experiment springs:

Two springs in a vertical position, in between a mass and a small Blech on it. If the mass is too much elongated, then the Blech will jump of the mass. (Because it is only accelerated with g from gravity and not by the springs)

Newton’s second law.

Newton’s third law.

Experiment Skateboard and medicine ball.

A student, standing on a skateboard and throwing a medicine ball backward is pulled forward by the medicine ball.

Break

Introduction to “data logger” and a first measurement of accelerations

Four groups of students took the data vests to different elevators in the building and measured a_x, a_y, a_z, and air pressure.

Discussion of the data, taken in the elevators

Which forces act in an elevator accelerating upwards, downwards?