BULL'S EYE

PURPOSE

Predict where a steel ball will land when released from a certain height.

The final test of your measurements and computations will be to position an empty soup can so that the ball lands in the can the first time!

• ramp or Hot Wheels track
• 1/2-inch (or larger) steel ball
• empty soup can
• meterstick
• plumb line
• stopwatch, ticker-tape timer; or computer light probes with interface light sources

Imagine a universe without gravity. In this universe, if you tossed a rock where there was no air, it would just keep going--forever. Because the rock would be going at a constant speed, it would cover the same amount of distance in each second. The equation for distance traveled when motion is uniform is

x=vt

Then speed is

v=x/t

Coming back to earth, what happens when you drop a rock? It falls to the ground and the distance it covers in each second increases. Gravity is constantly increasing its speed. the equation of the vertical distance y fallen after any time t is

y=1/2gt(squared)

where g is the acceleration due to gravity. The speed v after time t is

v=gt

What happens when you toss the rock sideways? The curved motion that results can be described s the combination of two straight-line motions: one vertical and the other horizontal. The vertical motion undergoes the acceleration due to gravity, while the horizontal motion does not. The secret to analyzing projectile motion is to keep two separate sets of books: one that treats horizontal motion according to

x=vt

and the other that treats the vertical motion according to

y=1/2gt(squared)

Horizontal motion

• When thinking about how far, think about x=vt.
• When thinking about how fast, think about v=x/t.

  Vertical motion

• When thinking about how far, think about y=(1/2)gt(squared).
• When thinking about how fast, think about v=gt.

Step One: Assemble your ramp. Make it as sturdy as possible so the steel balls roll smoothly and reproducibly. the ramp should not sway or bend. The ball must leave the table horizontally. Make the horizontal part of the ramp at least 20cm long. The vertical height of the ramp should be at least 30 cm.

Step Two: Use a stopwatch or light probe to measure the time it takes the ball to travel, from the first moment it reaches the level of the tabletop to the time it leaves the tabletop. Divide this time interval into the horizontal distance on the ramp to find the horizontal speed. Release the ball from the same point (marked with tape) on the ramp from each of the three runs.

1st time	2nd time	3rd time	Average time

Do not permit the ball to strike the floor! Record the average horizontal speed of the three runs.

horizontal speed calculation:

 

Step Three: Using a plumb line and a string, measure the vertical distance h the ball must drop from the bottom end of the ramp in order to land in an empty soup can on the floor.

1. Should the height of the can be taken into account when measuring the vertical distance h? if so, make your measurements accordingly.

 

 

 

 

h=____________

Step 4: Using the appropriate equation from the discussion, Calculate the time it takes the ball to fall off the table and land on the floor. Write the equation that relates h and t.

Which equation for vertical distance? _____________

Show your work in the following space.

 

 

 

 

t=______________

Step 5: The range is the horizontal distance of travel for a projectile off the table. predict the range of the ball. write the equation you used and your predicted range.

equation for range:________________

predicted rage R:__________________

Place the can on the floor where you predict it will catch the ball.

2. Compare the actual range of the ball with your predicted range. Compute the percentage error.

 

 

 

3. What may cause the ball to miss the target?

 

 

 

4. You probably noticed that the range of the ball increased in direct proportion to the speed at which it left the ramp. The speed depends on the release point of the ball on the ramp. What role do you think air resistance had in this experiment?

 

 

 

 

 

GOING FURTHER

Suppose you don't know the firing speed of the steel ball. If you go ahead and fire it, and then measure its range rather than predicting it, you can work backward and calculate the ball's initial speed. This is a good way to calculate speeds in general! Do this for one or two fired balls whose initial speeds you don't know.