PURPOSE:
To expose the student to new equipment and lab procedures. And to calculate the sum of two velocities (vectors) of a falling object in the laboratory.

INTRODUCTION:
A body's velocity is a directional value, with not only a magnitude but also a specific direction. You could be riding in a car with a velocity of 55 mph in a westerly direction. Saying you have a velocity of 55 mph is actually giving just your speed. In a 2 dimensional plane, moving bodies have an X and Y direction component to their velocity. This velocity can be thought of as a vector and the two terms are interchangeable. If a body is traveling in a purely horizontal direction (right) at 5 meters/second, it has an X velocity of 5 m/s and a Y velocity of 0 m/s. Likewise a purely vertical movement of 5 m/s has a Y velocity of 5 m/s (down) and an X velocity of 0 m/s. If a body is moving at 5 m/s in a horizontal direction (right) and at the same time 5 m/s in a vertical (down) direction, what magnitude velocity would this represent.

The Pythagorean Theorem, a² + b² = c², can be rearranged to: c = sqrt(a² + b²) and the resultant vector (velocity) can be determined. In this case, c = sqrt(25 + 25) = 7.07m/s. We now have the magnitude but in what direction? The angle that this vector will be oriented to can be calculated by using the equation:

vector angle = arctan(Y vector / X vector)

and in this case, vector angle = arctan(25/25) = 45 degrees below horizontal. In this lab we will be dealing with these principles since all X velocities are horizontal (right) and all Y velocities are vertical (down). The process of calculating the magnitude of the resultant vector gets a bit more complex if the two velocities are not purely horizontal and vertical, but is not covered in this lab.

NOTE: since the vertical component in the above example is traveling in a downward direction, its velocity would actually be -5 m/s and the vector angle would be -45 degrees.

If distance traveled by a body and the time it takes to travel this distance is also given, velocity can be calculated. The equation:

v = displacement / time

can be used where displacement = position final - position initial. The velocity needs to be constant and linear, as in this lab, for this to be correct.

Another twist that can be added to this type of problem is to make one of the velocities an acceleration. Gravity is a common acceleration in a vertical (down) direction and is used often for the vertical component of movement. The velocity (Y direction) of the body can be calculated using the equation:

v = v₀ + at

where v₀ is the initial velocity, which is normally 0, a is gravity, 9.80 m/s² and t is the time in seconds from the initial v to this final v. More hints on these calculations are listed in the lab.

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The horizontal velocity for our object is generated by the above spring loaded gun. The plunger is pulled to the left until it latches in place. When the release button is pressed the object is driven to the right at a constant velocity.

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A large background screen is provided to map the progress of our moving body. The squares of the screen are 5 cm x 5 cm in size.

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A digital camera is provided to record the path of our moving object. A strobe flash on top of the camera is set to fire every 0.10 seconds freezing the image of the falling object at that instant. Between flashes the body moves but no pictorial record is made.

 

If you get into trouble and perform some procedure that causes the lab to fail(lab equipment will no longer operate), you can press the "Reset" button and the simulation will return to the starting position.

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PROCEDURE:

1) You can adjust the background shading by clicking on the "Special" button to the right and selecting "Background". Click on the "Special" button and select "Print Blank Report" to obtain a web page that can be printed and used as a lab report. (the program will not be interrupted)

Note: In this lab we wish to measure the horizontal and vertical movement of a falling ball. A way to do this is to photograph the ball as it moves with a timed strobe light. In this way, the position is recorded at set time intervals. If we turn off the room lights, the in between positions of the ball will not be captured by the camera.

2) In the upper left of the screen is located a blue spring loaded gun. Grab the red knob on the left side of the gun and pull back until it latches. This sets the spring and the gun is now ready to fire. Pick up the red ball, on the table, and drop it in the center of the gun. Pick up the camera and tripod and position it in the center of the background screen to the right.

3) The camera is on but in order to take a series of "stop action" photographs we must first turn the room lights off. Click on the "Special" button and then press background until the lights are off. Click on the red button located on the strobe light above the camera to start the strobing light. These flashes are 0.10 seconds apart and form the timer for our photograph. Click on the lever atop the spring gun to release the plunger starting our ball on its journey.

4) When the ball comes to rest on the table, turn off the strobe. Go to the next room.

5) Here is your finished photograph capturing the position of the ball every one tenth of a second.

6) Calculate the requested values asked for on the lab sheet and any given by your teacher. For help on these values click on the "Special" button and select "View Data & Hints". Select "File Report" to send a copy to be viewed by your teacher.