11 Septmeber 2014: Trajectories Lab 5

Objectives:
1) Study the components of motion in projectile motion.
2) Use our understanding of projectile motion to predict the landing point of a ball on an inclined board

Materials:
1) 2 Aluminum v-channels
2) 1 steel ball
3) Board
4) 1 Ring stand and clamp
5) Tape
6) Carbon Paper
7) 2 Blocks of wood to hold one of the aluminum v-channels
8) Plumb bob (weight and string) (optional)
9) Ruler

Set up:

As you can see the horizontal v-channel is held in place by the 2 blocks of wood. The v-channel at an angle is held in place by the ring stand and clamp. Also, it is held in place by tape at the bottom so it does not slide while the ball is rolling down it.

As you can see from this pictures, in addition to the set up on the table top, we also taped carbon paper to the floor to document where exactly the ball lands. We also hung a plumb bob (weight and string) from the edge of the table.











Procedure:
Part 1: Now that our setup was complete, we launched the ball from the v-channel at an angle. We marked the exact spot from which we launched it the first time and launched it from the same spot another 5 times. Remarkably, the ball landed in exactly the same spot all 5 times:

I added a red circle to clearly identify the mark of the landing point of the ball

We were then asked to determine the height from the table to the floor and the distance from the table's edge to the mark. We used a ruler to determine these measurements and can be seen below:

horizontal v-channel=31.5 cm, height= 93 cm, distance from table to mark=47.2 cm

We were then asked to determine the launch speed of the ball when it leaves the table. The calculations can be seen below:

v0= 1.08 m/s

Part 2: We were then asked to imagine attaching an inclined board at the edge of the table in a set up that looked something like this:

We were then asked to derive an expression that would allow us to determine the value of d. Our calculations of this expression looked like this:

We then actually ran the experiment by placing the board against the table and taping the carbon paper to the board. We then measured the angle that the board created with the floor and found the angle to be 45 degrees. We then launched the ball five times from the exact same spot. Our experimental d was found to be 0.31 m.

We then determined our theoretical d. Our calculations can be seen below:

d=0.33 m

We were able to determine our v0 from part one and plug into our calculations for part 2. Overall, these were our values:

experimental d= 0.31 m

theoretical d= 0.33 m

Conclusions:
If we were to create a percent error with our results it would look like this:

Percent Error= 0.31-0.33   x 100% = 6%
                                0.33

Our percent error was 6%. There were sources of error that could account for this percent error. Sources of error might lie in the rotational friction from the track that was not accounted for. It was also difficult to exactly measure distances from the table edge.