**Physics Day**

**at**

**Lake Winnepesaukah**

produced by

Randolph S. Peterson and

the physics teachers of the Physics Alliance of Chattanooga

**Roller Coaster**

This ride is wonderful for studying kinetic and potential energies, and for measuring the "g forces" that riders experience.

**Kinetic and Potential Energy**

Measure the height of the first hill on the track (using trigonometric relationships). Compare your results with your Physics Coach's results.

height = .................meters

Estimate the mass of the car and rider = ....................kg

(Ask the operator for a hint.)

Your estimate of the highest speed obtained from the kinetic energy of the car is

.........................meters per second

The advertisements say that this roller coaster travels at speeds up to 55 mph (which is 24.6 m/s). Is this reasonable?

The height of the second highest hill (hill #3) is 50 feet (=15.2 m). How fast are you traveling at the top of this second highest hill?

speed at the top of the second hill = .....................m/s

**Acceleration and "g forces"**

Use the vertical accelerometer to measure the "g forces"
at the top and at the bottom of the first and second highest hills.
If you hold the accelerometer in the wrong orientation, you must
ride the ride again! Please estimate your answers before riding
the ride. The acceleration needed to move you along the circular
path is v^{2}/R.

..................................................................estimated............................... measured

acceleration at the top of highest hill = ....................g ............................................g

acceleration at bottom of highest hill = ...................g ............................................g

acceleration at the top of second hill = ....................g ............................................g

acceleration at bottom of second hill = ...................g ............................................g

An acceleration of 3 g's is a typical acceleration experienced on launch by space shuttle astronauts.

Use the CBL with the 3D accelerometer to measure your acceleration every 0.1 seconds for the entire 90 second ride on the roller coaster. Reconstruct the shape of the roller coaster path from your acceleration data. This is a project for the classroom.

**Ferris Wheel**

In order to move in a circular path you must experience a net force directed toward the center of motion. At the top and bottom of the ride, this force is colinear with your weight. You can feel the force, so why not measure it.

Ride the Ferris wheel while sitting on a bathroom scale**.
**Measure the force**!**

Measure or estimate the following values

Radius of the motion of the gondola = R = ....................meters

Average time for one revolution = ................................seconds

Your at-rest sitting weight (pounds) x 4.45 = W_{o}

W_{o} = .........................Newtons

Your sitting weight at the top while moving (pounds)

x 4.45 = ......................Newtons

Your sitting weight at the bottom while moving (pounds)

x 4.45 = ........................Newtons

**Calculate**

Speed of the gondola = ....................m/s (=2 p R/T)

The force that you exert on the bathroom scale at the bottom is

F = mg + mv^{2}/R = ...................Newtons

The force that you exert on the bathroom scale at the top is

F = mg **-** mv^{2}/R = ..................Newtons

m is your sitting mass, m = W_{o} /g. Use g = 9.8 m/s^{2}.
By substitution, these two equations can be written

F = W_{o} +/**-** W_{o}v^{2}/Rg
= W_{o} (1 +/**-** v^{2}/Rg)

Do you feel lighter at the top or the bottom? Does this agree with your calculations above?

**Merry-Go-Round**

**Speed**

This ride starts from rest and accelerates to a constant angular speed, w. However, your actual speed depends upon how far you are standing from the center of the ride. Let's measure and calculate these quantities. To determine the angular speed, we need the period of revolution. Measure the time for 2 complete revolutions and divide by 2 to obtain the average period of revolution, T.

w = 2 p /T = 6.28/T = ...................radians per second

w
= 360^{o}/T = ................................degrees
per second

We need w in units of radians per second for our next calculation. Your actual speed, v, at any position on the ride is

v = R w =....................... meters per second

= ....................................miles per hour

where R is your distance from the center of rotation. Estimate the distance, R, while the ride is stopped. Note that 15 mph is

6.7 meters/sec, and 30 mph is 13.4 meters/sec.

**Accelerations and Forces**

Sit in the sled and place the tennis ball on the floor of the ride. Which direction does the tennis ball roll when the ride is stopped and when the ride is moving?

Ride stopped .............rolls toward center .............toward outside

Ride moving ............ rolls toward center............. toward outside

The 57 gram (=0.057 kg) tennis ball experiences a force directed
toward the center of the ride of about 0.1 Newtons. For the ball
to move on a circular path and appear to stay in one place at
your feet, this force must be equal to F = m R w^{2}. If the force
F needed to move in a circular path is greater than 0.1 N then
the ball will roll to the outside. Calculate F from your measurements.

F = m R w^{2} = ..................N

**Relativity in the Park**

Einstein's special theory of relativity is based upon just
a few ideas - the speed of light in a vacuum is the same for all
observers, and there is no experiment that can determine which
of two frames of reference is moving absolutely, if those frames
are inertial frames. An inertial frame is a place that is moving
in one direction at constant speed. **The Merry-Go-Round is not
such a place.**

Have a friend ride the Merry-go-round with you. Take a tennis ball from a Physics Coach on the ride. Position yourselves in a safe position to be able to roll the tennis ball back and forth to each other. The floor inclines toward the center just a bit, so you may expect so curvature in the balls path.

From the point of view of the person rolling the ball, which
direction does the ball deflect (to the **right** or the **left**)
when the ride is moving? Does it matter whether you are rolling
the ball tangent to your motion or perpendicular?

direction = __________________

Discuss with a Physics Coach or your class afterwards whether the Merry-go-round is an inertial frame and why you think so.

A frame of reference attached to the surface of the earth is not an inertial frame. The effects can be seen in the Coriolis effects we call hurricanes and tornadoes.

**Swinging Pirate Ship**

This ride is very similar to the Ferris wheel and the roller coaster, and the accelerations that you experience are just the ones to move you along a circular path. In addition, this swinging ship is a pendulum, which should be a well-studied example from your physics textbook and physics lab.

Pendulum

If you remember the simple pendulum results, the period of oscillation, T, for a pendulum of length L is

T = 2 p (L/g)^{0.5}

**Estimate** the length of the pendulum and **measure**
its period.

Length (L) = ________m

Period (T) = ________sec

How well does the simple pendulum equation predict the period when the oscillations are not small and the pendulum is not simple? Calculate the period expected for a simple pendulum.

Period calculated from the pendulum's length = ___________sec

Does the theoretical prediction agree with your measurement, within 5%?

Just like the Ferris Wheel, the force you experience at the bottom of the ride can be measured as a change in your weight.

Ride the Pirate Ship while sitting on a bathroom scale**.
**Measure the force**!**

**Accelerations**

Measurements of the "vertical" accelerations reveal some amazing accelerations! Where do you predict the accelerations to be the greatest when the ride is moving, and in what direction are the accelerations? Check one.

____At the top of the swing

____At the bottom, the "resting position"

Where is your speed on the ride **zero** meters per second,
during the time the ride is being operated? Check one.

____At my highest position above the ground

____At my lowest position above the ground

____Never

**Measure or estimate the following values**

Your at-rest sitting weight (pounds) x 4.45 (N/lb) = W_{o}

W_{bot} = ____________Newtons

Your sitting weight at the bottom while moving (pounds)

x 4.45 (N/lb) = W_{bot}= ____________Newtons

**Calculate**

Your weight at the bottom of the ride's motion is

W_{bot} = (W_{o}/g)**a** , so that your
acceleration is

**a** = (W_{bot}/W_{o})g = _____g = ________m/s^{2}

IF you measured the acceleration with a vertical, spring accelerometer, how do the two measurements compare?

**a** (from spring accelerometer) = __________g