Lab – Bull’s Eye

**Purpose**

To investigate the independence of horizontal and vertical components of motion. To predict the landing point of a projectile.

**Required Equipment/Supplies**

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Ramp

˝” (or larger) steel ball

small cup

meterstick

plumb line

stopwatch or

Photogate

TI 83+ w/ Datagate pgrm

**Discussion**

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An object that is 5 m above the ground will take one second to fall to earth when dropped. And an object 5m above the ground will take the same time to fall even if it is launched or thrown horizontally. In today’s lab you will calculate the speed of a marble coming off the ramp and the time of decent based on the height of your lab table. With these two measurements you can accurately predict where the marble will hit the floor when allowed to roll down the ramp and off the table. Good luck!

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**Procedure**

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**Step 1**
(compute the horizontal speed):
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 20 cm long. The vertical height of the ramp should be at
least 30 cm.

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**Step 2**
(compute the horizontal speed): Use a
stopwatch or photogate to measure the time it takes the ball to travel from the
first moment it reaches the level of the table top to the time it leaves the
table top 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 for each of three runs.

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

Horizontal speed = __ __

**Step 3**
(measure the vertical distance): Using
a plumb line and a string, mesure 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* = __ __

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**Step 4**: Using the appropriate equation from the
discussion, find the time *t* it takes
the ball to fall from the bottom end of the ramp and land in the can. Wright the equation that relates *h* and *t*.

Equation for vertical distance: = __ __

Show your work in
the following space.

**Step 5**
(predict the range): The range is the
horizontal distance of travel for a projectile. Predict the range of the ball.
Write the equation you used and your predicted range.

Equation for range: = __ __

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Predicted range *d*:
= __ __

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

**Step 6** (test your prediction): After I have checked your predicted range
and your can placement, release the ball from the marked point on the
ramp. See whther the ball lands in the
can.

**Analysis**

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2. Compare
the actual range of the ball with your predicted range. Compute the percentage error. (We’ll discuss the formula)

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?

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