23 March 2015. Trajectories.

Purpose
to predict (calculate) the impact point of a ball on an inclined board with the understanding of a projectile motion.

Apparatus:

1. Aluminium "v-channel". This is some sort of a v tunnel that can let the ball roll down.
2. Board, ring stand, and clamp. Apparatus 1 and 2 are going to be set up as shown below.

3. Steel ball. This ball is going to be used as the object of the projectile.
4. Paper and Carbon paper. These paper are going to be piled up together with the carbon on top, so that when the pressure from the weight of the ball acts on the paper, the carbon paper would leave black marks onto the normal paper.
5. Angle measurement apparatus: a device that is used to measure angle (shown below).

Angle Measurement

Procedure:

The steel ball will land onto the paper.

1. Launch the steel ball from a identifiable and repeatable from the inclined ramp and take a notice where it hits the floor.
2. Tape a piece of carbon paper to the floor around the ball landed. Thus, it will leave marks onto the paper. Do it five times and measure the average distance.
3. Also measure the initial height when the motion of trajectories start.
4. Record this value.
5. Change your set up into number 2 picture shown in the apparatus section.

Distance recorded (on the floor)

1. Then use another inclined board at the edge of the lab table, and by doing this the ball will now hit the inclined table instead of the floor. Measure the angle.
2. Also put some carbon paper and measure the distance of this trajectories motion. Compare it with the calculation you got by doing the first part of the experiment.

Measuring the angle of the inclined board

launching the steel ball from an identifiable spot

Distance recorded (inclined board)

Data Analysis:

• Below is the collection of data we recorded.

• Now, from the first two data, we measure our initial speed and what distance should it cover in the second set up with this speed.

• Using d, we calculate the distance.
• Now that we got the result, lets calculate the propagated error of this distance.

• This is how we derive the partial derivative of distance to the angle.

• Now,  we compare the true and experimental value.

Conclusions:

• In this experiment, we use the understanding of projectile motion to estimate where the ball hits the inclined board. 
• In the first part, we use projectile motion to calculate the launching speed of the ball. The result we got is v_ox = 1.23 m/s. 
• As we got the value for the speed, we continue part 2 to determine the distance on the inclined board where the ball hits it. The experimental value we got is 0.556 m, the theoretical value calculated is 0.544 m ± 0.00999 m.
• Next, we calculated the percent error to see how far we are off from the "true" value. Our result is %error = +2.072% which is sufficiently good.
• The small percent error shows that we didn't perform many errors while doing the experiment. Some of small errors might be cause by human errors such as not being precise enough when measuring the distance, slipping to put right into the original spot for the steel ball which may cause different initial velocity, and many more.