general physics lab edit

Physics Online Projectile Motion

Introduction

The purpose of this lab is to test the 2-d kinematics equations. The one dimensional constant acceleration kinematics equations can be extended to two dimensions as follows:

x	y
vfx = vox + axt	vfy = voy + ayt
Δx = voxt + ½axt2	Δy = voyt + ½ayt2
vfx2 = vox2 + 2axΔx	vfy2 = voy2 + 2ayΔy
Δx = ½(vox + vfx)t	Δy = ½(voy + vfy)t
Δx = x-component of displacement vector	Δy = y-component of displacement vector
vox = x-component of initial velocity vector	voy = y-component of initial velocity vector
vfx = x-component of final velocity vector	vfy = y-component of final velocity vector
ax = x-component of acceleration vector	ay = y-component of acceleration vector
t = time interval	t = time interval

These equations are valid when the acceleration vector is constant throughout the time interval. Note that the equations for x and y look similar, with only the subscripts changed. Also note that these general equations are consistent with the more specific equations listed in your textbook.

In our experiment, we will study the motion of a projectile. Since the projectile will be in free-fall after launching until impact, we know the acceleration vector will be:

ax= 0

ay = -g = -9.8 m/s2

The value of g will depend on location, so you may need to adjust this value to your local condition.

Equipment You Procure

· tape measure

· tape

· 3 hard horizontal surfaces of different heights (table, countertop, dresser, etc.) that do not have beveled edges

· digital camera

· paper

· pencil or dry erase pen

· action figure or Lego mini-fig (optional)

Equipment from Kits

· inclined plane

· 4” x 6” card

· solid metal sphere

· bubble level

Experimental Procedures

Horizontal Launch Speed Calculation

1. Select a horizontal surface. Use the bubble level to check if the surface is horizontal. If the surface is not horizontal, then correct this or select another surface.

2. Raise the inclined plane to an angle between 20° and 45°.

3. Tape the 4”x6” card to the end of the inclined plane. An inch or two of the card should overlap the end of the inclined plane.

4. Place the inclined plane on the horizontal surface so that the non-taped end of the card is a few inches from the edge of the horizontal surface.

5. Measure the vertical distance between the top of the surface and the floor, Δy.

6. Place a solid metal ball at the top of the ramp and release it. It should roll down the ramp, across the card, across the horizontal surface a couple inches, launch horizontally, and land on the floor. Note the approximate landing place of the ball.

7. Tape down a piece of paper centered near the landing place.

8. Draw all over the metal ball so that it will make a mark on the piece of paper when it lands.

9. Roll the metal ball down the ramp again.

10. Measure the horizontal distance between the edge of the surface and the landing place, Δx.

11. Use kinematics in the y-direction to calculate the time to impact, t. You should already know ay (assumed), voy (assumed), and Δy (measured), so use an equation that includes those three variables plus the variable of interest, t. Note that Δy and ay will be negative using a conventional coordinate system.

12. Use kinematics in the x-direction to calculate the launch speed, vox. You should already know ax (assumed), Δx (measured in step 10), and t (calculated in step 11), so use an equation that includes those three variables plus the variable of interest, vox.

Predictions of Horizontal Distances Based on Launches from Different Heights

0. Select a different horizontal surface at a significantly different height.

1. Use the bubble level to check if the surface is horizontal. If the surface is beveled or not horizontal, then correct this or select another surface.

2. Place the inclined plane on this surface so that the non-taped end of the card is a few inches from the edge of the horizontal surface.

3. Measure the vertical distance between the top of the surface and the floor, Δy.

4. Use kinematics in the y-direction to calculate the time to impact, t. You should already know ay (assumed), voy (assumed), and Δy (measured in step 16), so use an equation that includes those three variables plus the variable of interest, t. Note that Δy and ay will be negative using a conventional coordinate system.

5. Use kinematics in the x-direction to calculate the theoretical horizontal distance, Δx. You should already know ax (assumed), t (calculated in step 17), and vox (calculated in step 12), so use an equation that includes those three variables plus the variable of interest, Δx.

6. Tape down a piece of paper or place your action figure at the predicted landing place.

7. Draw all over the metal ball if you are using paper.

8. Roll the solid metal ball down the ramp.

9. Note if you hit your action figure OR measure the horizontal distance between the edge of the surface and the landing place, your experimental Δx, and compare it to your theoretical value.

10. Repeat steps 13 through 22 with a surface of a significantly different height.

Different Launch Speed

0. Repeat steps 1 through 23 with a different ramp angle or with the ball released from somewhere besides the top end of the ramp. This will give a different launch speed. This will give you a total of 6 measured launches, and 4 comparisons of theoretical and experimental distances (or 4 attempts to kill your action figure). If you do not have 6 measured launches (2 different ramp heights x 3 different surface heights) and 4 comparisons of theory and experiment (or 4 attempts to kill your action figure), you will have your report returned for revision. See the following table and check that you have made all the necessary measurements and calculations:

Measured	Assumed	Calculated
Ramp Angle #1 Δx (experimental) Δy #1	voy ax ay	t vox
Ramp Angle #1 Δx (experimental) OR note of hit/miss Δy #2	vox voy ax ay	t Δx (theoretical)
Ramp Angle #1 Δx (experimental) OR note of hit/miss Δy #3	vox voy ax ay	t Δx (theoretical)
Ramp Angle #2 Δx (experimental) Δy #1	voy ax ay	t vox
Ramp Angle #2 Δx (experimental) OR note of hit/miss Δy #2	vox voy ax ay	t Δx (theoretical)
Ramp Angle #2 Δx (experimental) OR note of hit/miss Δy #3	vox voy ax ay	t Δx (theoretical)

Notes: Do not include the above table in your report. The instructions do not include a statement that you should include a graph, so you should not include a graph. You may skip uncertainty propagation in this lab. You must still include uncertainty estimations for all raw data. Your conclusion will include a subjective assessment of whether or not the predictions were “close”.