Fire Away!

Our Design:

Our team made multiple modifications to our catapult from changing the axle height to changing our pillar angle. Some of the modifications yielded to a very prominent positive result as others amounted to no effect. The modifications to the catapult are as follows:

1. Projectile Mass

The mass of the projectile should be 7-10 grams (¼ -⅖ oz) for the farthest distance. If the mass of the projectile is excessive, then it will not reach as far as a 7-10 gram projectile, because a heavier mass is harder to move because of inertia,the tendency of an object to remain in its initial state, until acted upon by an outside force. Since the mass begins in a rest position, it is harder to move because it takes more work to move it from a stationary state to an active state. In addition, if the projectile of insufficient mass is fired, it will experience wind resistance or drag, as it doesn’t have enough inertia to continue moving forward, which slows the velocity of the projectile, making it cover an exponentially lesser amount of distance over time. Thus the happy medium is a mass of 7-10 gram for the projectile, as it has enough mass to not be affected as much by drag

2. Nail Angle on the Load Side

From experimentation, we have concluded that the angle of the nail should be 10° backwards from perpendicular of the arm’s end, if it is a finishing nail. The nail being bent at 10° backwards makes the angle of release close to the ideal 30-45°. The reason why the ideal angle is between 30-45°, is because the total velocity is evenly placed, making the projectile move farther, the 30° accounts for the fact that gravity will pull the projectile downwards, so angling the projectile higher, should mostly balance the effect. The nail is bent 10° backwards because of two reasons:

• The string connected to the projectile needs to be still attached to the nail, so 10° backwards makes it so that the nail can still catch the string, without falling off.

• The angle keeps it closer to the ideal of 30-45°, that will allow for the longest distance, for the projectile to travel.

3. Stopper vs. No Stopper

Not having a stopper for the catapult does not make a difference in the launch of the projectile. The main reason why having a stopper and not having a stopper does not affect the distance the projectile travels is because, the projectile is already launched before being stopped. The projectile leaves because the projectile’s inertia is mostly vertical, but it is moving along a circular path. This makes it leave before hitting the stopper because of the projectile’s tendency to continue to move vertically than horizontally in a circular motion Regardless of whether a stopper is included in a catapult’s design does not affect the distance the projectile travels, as the projectile leaves the nail before the stopper releases the projectile.

4. String Length

The length of the string attached to the projectile should be 35-40 cm (13 ¾- 15 ¾ in.) total or after tying a knot at halfway, 17.5-20 cm (6 ⅘ - 7 ⅖ in.). This length of string allows for the arm to pull the string, indirectly pulling the load of the projectile. Moreover, this makes it so that the projectile is traveling a longer distance at the same amount of time, increasing its velocity, increasing the distance the projectile can travel. If the string is too long, then the arm will not be able to effectively move the projectile as the arm needs to rotate more to catch the string, and the arm wastes energy that could be used to drive the projectile. If the string length is too short then the velocity of the projectile is decreased as it travels a lesser distance over the same amount of time. Therefore a total string length of 35-40 cm is required for a projectile, to increase the velocity of the projectile, and have it be long enough for the string to catch the nail and be able to fire the projectile effectively.

5. Pillar Angle

The angle of the pillars, or the legs, of the catapult has no effect on the distance the projectile obtains. A pillar angle of 75° does not affect the distance the projectile travels, as the axle is still in the same position in height whether there is an angled pillar or not. Thus the angle of the pillar has no effect on the distance traveled by the projectile, and can be used as an aesthetic feature.

6. Mass of firing ball: And lastly, we changed the mass of the firing ball. According to a 2 studies conducted by other groups in our class, the best mass for the firing ball would be between 7 to 10 grams. Following this experiment, we had to choose a mass between 7 and 10, so we stuck with 8 grams.

Reflection

From this project, I have gathered more experience than the previous ones, even though this project had only lasted a week. I thought the way we discussed circular motion in class was very effective, especially the explanation of how centrifugal force works, and why it is a ficticious force. I was also impressed with the total group productivity, with the given time frame, because in the past I had experienced issues with time management, this, I thought, was very interesting. We had construction and testing in progress within two days. With this, I also thought that job delegation and communication was poor amongst the group, but we still had a fleshed-out product. This can be attributed the participation of our group members, and the lack of a brainstorming session. It was our close-mindedness, and even sometimes our unwillingness to share out our ideas, that distanced each group member from each other, and worsened the communication of the group. In all, the project and classwork was very effective in teaching the concepts of circular motion, and the project as a whole went well.

Mass of the projectile

0.004kg

Total Time in Air

2.25s

Horizontal Distance

24m

Vertical Distance

5.9m/s

Horizontal Velocity

10.9m

Vertical Velocity

5.5m/s

Total Velocity

11.99m/s

Angle of Release

25.1*

Spring Constant

1500N/m

Initial Spring Potential Energy

36.3N

Kinetic Energy of Projectile

0.29N

Percent of Energy Converted

8%