125 Physics Projects for the Evil Genius (7 page)

Figure 5-2
“Skateboard” accelerometer
.

A pendulum hangs vertically when moving at constant velocity. But it moves in the
opposite
direction as the acceleration it is experiencing. If an object slows down or decelerates, it shows up as a backward movement in the pendulum.

Figure 5-3
Floating bob accelerometer
.

When the apparatus with the floating bob is spinning, the bob moves inward. This may be the opposite of what you might expect and is the opposite of what would happen with a freely hanging pendulum. The reason for this is the centripetal acceleration increases the buoyant force on the bob, forcing it inward. Candles move in the opposite direction. The flame moves outward, as does liquid in a container.

Newton’s second law requires that force and acceleration are related to each other through F = ma. If there is acceleration (a), there is a force (F) on the moving object (or mass, m). The force is in the same direction as the acceleration.

An accelerometer, such as shown in
Figure 5-4
, directly indicates acceleration with a set of LEDs that light in proportion to the amount of acceleration. The greater the acceleration, the more LEDs will light. It can, for instance, indicate the acceleration of a cart pulled by a string. It can also be used to monitor centripetal acceleration.

A hanging (or other unconstrained) object is affected by acceleration, but is
not
affected by uniform steady velocity.

Figure 5-4
An applied force causes an object to accelerate. Courtesy PASCO
.

When exposed to the force of gravity, objects fall faster and faster. This is called gravitational acceleration. When objects fall straight down, you have to be very quick if you want to measure how long an object falls a given distance. When Galileo Galilei tried to do this during the fifteenth century, he used primitive timing devices, such as dripping water and his own pulse to keep track of objects dropped from the Leaning Tower of Pisa. To overcome the difficulty of timing these measurements, Galileo had the brilliant insight of slowing down gravitational acceleration using a ramp. In this experiment, you follow in Galileo’s footsteps. However, you have the advantage of being able to use a stopwatch or even a motion sensor to more accurately measure the object’s movement.

• inclined track (such as a section of wooden corner molding, semi-round vinyl bullnose molding, or a flat board with two “gutters” created by attaching metersticks as guides)
  
• golf balls or marbles
  
• stopwatch or other timer
  
• meterstick
  
• optional: motion sensor, inclined air track
  

1. Set the inclined track at a moderate angle with respect to the surface on which it is supported.

2. Mark distance intervals from the bottom of the track in 10 cm increments.

3. Release the golf ball (or marble) from each of the distances marked and record the time in seconds that it takes to reach the end of the ramp. See
Figure 6-1
.

Figure 6-1
Ramp used to measure effects of acceleration
.

4. If you measure the distance the ball rolls and the time it takes to roll, you can easily find the acceleration,
a
, at any point using a = 2d/t
²
, where
d
is the distance it rolls and
t
is the time it takes to roll that distance.

5. What is the effect of changing the slope of the incline on the rate of acceleration?

A graph of distance versus time, such as pictured in
Figure 6-2
, shows that the distance the object moves
in a given amount of time
is increasing. The distance in the graph is shown to increase as the
square
of the time which is a characteristic of constant acceleration.

When an object accelerates, its velocity changes with time. For the case of constant acceleration, the velocity increases by a constant amount every second. This results in the distance increasing as the square of the time.

A rolling golf ball or marble can be considered a falling object whose acceleration is slowed by the incline. This is approximately, but not completely, true. Any rolling object develops angular momentum that ties up some of its energy in the process of rolling.

Figure 6-2
Distance versus time for a golf ball rolling down an incline
.

Figure 6-3
An air track with a motion sensor attached to the end. Courtesy PASCO
.

Better precision can be achieved by using an air track. This reduces the impact of friction and rotational kinetic energy. Incorporating a motion sensor to measure velocity and acceleration adds another dimension, as
Figure 6-3
shows.

DataStudio software displays the distance measured by the motion sensor, as shown in
Figure 6-4
.

When an object accelerates, its velocity changes with time. If that acceleration is constant, distance increases as the square of time.

Figure 6-4
Position (in meters) versus time (in seconds) for three different inclines. Courtesy PASCO
.

Which will hit the ground first: a bullet dropped straight down from a height of 5 feet or a bullet fired horizontally over flat ground at 300 m/s from the same height? Many people guess that the greater momentum of the moving bullet would keep it in the air longer. This experiment addresses this question.

A
projectile
is an object that has both horizontal and vertical motion. Although motion in two dimensions may seem very complicated, it can be enormously simplified based on the results of this section. You discover that the horizontal motion of a projectile is completely independent of its vertical motion. It does not matter how fast an object is falling. In this experiment, you prove this in several ways.

• chair
  
• basketball
  
• someone willing to sit in a chair
  
• independence of horizontal and vertical motion apparatus
  
• ballistic car
  

This is simple to do, but it has a significant result.

1. Have the person sit in the chair holding the basketball.
   
2. Roll the chair (with the person sitting). The person can alternatively be on a skateboard or roller blades.
   
3. Have the person toss the basketball up and observe its trajectory.
   

1. Place a coin at the edge of a table.
   
2. Flick a second coin toward the first so that the first is just pushed over the edge and the second coin flies off the table.
   
3. Both coins should start falling at the same time. One with a horizontal velocity and one without.
   
4. Listen to see which, if any of the coins, strikes the floor first. Repeat this enough times until you get consistent results.
   

Use a commercially available apparatus, such as pictured in
Figures 7-1
and
7-2
. The apparatus shown in
Figure 7-1
is much easier to use. The ballistics car shown in
Figure 7-2
may require a level surface and some practice. A more reliable version of this is available as an accessory for an air track.