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INTRODUCTION

Projectile motion could be defined as the motion of an object launched at a certain speed and then subjected only to

the constant acceleration of gravity. Real-world examples are everywhere: bullets shot from guns, erasers hurled across classrooms, basketballs thrown into hoops, bottles tossed into garbage cans, pianos flung by trebuchets.

Projectile motion is a good subject for study because it describes a lot of real-world situations, and because the math involved is not especially difficult. To keep the math from becoming difficult, we make a few reasonable assumptions.

Galileo was the first person who accurately described projectile motion. Because of the drawings of Niccolo Tartaglia, Galileo realized that a projectile followed a curved path which is called a parabola. It was later found out by Galileo that the parabola has an exact mathematical shape. Also, he stated that a projectile was acted upon by two forces, vertical and horizontal. The vertical force was from gravity, which pulled it to Earth at 9.8 m/s. That is why a parabola is a precise mathematical equation.

The foremost of these assumptions is that gravity is the only force acting on the projectile.

In particular, we assume that there is no air resistance. That's a reasonable assumption, as long as the projectile is fairly dense and is not moving too fast through the air. It breaks down if the projectile isn't dense enough (e.g. a loose wad of paper flung across a room) or if it's moving far and fast enough to make air resistance a serious effect (e.g. an artillery shell fired a long distance at supersonic speed). These effects should not be a problem in this lab.

OBJECTIVE

To determine the acceleration due to gravity, g using motion method.

THEORY

From the law of the conservation energy, the potential energy of a body of mass, m equals to its kinetic energy and is given by:

mgh=12mv x

2

R=v x t

g= R2

2h t2

(1)

Where m = the mass of the object g = the acceleration due to the gravityh = the height of the bodyvx = the velocity of the body

A body which is moving in a projectile motion with a velocity of vx will have a range of:

(2)

Where vx is the horizontal component of the velocity (see in Figure 1)

Combining equation (1) and (2), we obtain:

(3)

Where t is time taken for the body from the end of the curve track to reach the ground.

Figure 1

h

pendulum bob

horizontal table

projectilemotion

drawing paper

curved railing

steel ball

steel ball

vxsteel ball

Procedure:1. Set up the apparatus as shown in Figure 1.2. Slide the steel ball on the curve railing from 8 different

heights, h and record the values of R and t.3. Plot a graph of R2 against 2ht2 and calculate the value of g

from the table and graph.

RESULT

NoHeight, h (m)

Range, R (m) Time, t (s)R2 T2 2ht2

R1 R2 R3 R T1 T2 T3 T

1 0.050.307

0.307

0.302

0.305

0.51

0.72

0.70

0.64

0.0930

0.41

0.041

2 0.100.459

0.456

0.464

0.460

0.51

0.47

0.46

0.48

0.2116

0.23

0.046

3 0.150.538

0.552

0.573

0.554

0.51

0.45

0.43

0.46

0.3069

0.21

0.063

4 0.200.642

0.666

0.668

0.659

0.42

0.41

0.49

0.44

0.4343

0.19

0.076

5 0.250.740

0.743

0.728

0.737

0.42

0.42

0.43

0.42

0.5432

0.18

0.09

6 0.30 0.82 0.82 0.80 0.81 0.4 0.4 0.4 0.4 0.667 0.1 0.10

8 0 2 7 0 1 3 1 5 7 2

7 0.350.882

0.892

0.847

0.874

0.40

0.42

0.39

0.40

0.7639

0.16

0.114

8 0.400.871

0.880

0.854

0.868

0.38

0.41

0.39

0.39

0.7540

0.15

0.124

DATA ANALYSIS

g= R2

2h t2

Graph 1.0

CALCULATION :

By using this this formula below, we can obtain the gravity based on the gradient of the straight line from the graph above.

Find the gradient for the best line.

𝑚𝑏 = g = y2− y1

x2−x1

= 0.70−0.280.11−0.06

= 8.4ms-2.

DICUSSION

The experiment was carried out to investigate the relationship between acceleration due to gravity, 9.81 ms-2. We

0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.130

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

R2 vs 2ht2

2ht2

R2

managed to obtain all the data by doing all the procedures as followed. Graph 1.0 was constructed based from the data table in order to obtain the gradient from the straight line which is being used to calculate the gravity. In this experiment, 8 different heights were set by using the curved railing to let the steel ball rolls down to the landing surface. The stopwatch was started when the steel ball reached at the end of the curved track and being stopped immediately after it reached the landing surface (carbon paper and drawing paper). All the observations were recorded in the table.

From the data table, it shows the velocity for each height is not constant. This is because the time and acceleration values for each height where the steel ball released were different. Because acceleration is the rate of change of velocity per unit of time, the velocity was changing, not constant. The time value would get smaller and the acceleration value would increase as the curvature railing got steeper. Also, while going down the curved railing, the ball changed its velocity. Therefore at each height, the velocity values were different and the velocity changed as the ball travelled down the curved railing.

As the calculation has been made, it can be found that the acceleration due to gravity is 8.4 ms-2, which was slightly different with the theoretical value for acceleration due to gravity which is 9.81 ms-2. The slight different might be caused by the air resistance and frictional force between curvature railing and the steel ball. The experiment can be said as successful because the difference between theoretical value of acceleration due gravity was small.

To ensure the observation of the data is more correct, the experiment needs to be repeated for three times to find the average value. Thus, the accuracy of the value obtained will be précised. Besides that, in order to reduce the error, our eyes must be perpendicular to the scale in order to avoid parallax error. Besides that, we must make sure the curvature railing was straight to ensure that the ball can slide in a straight line. The stopwatch needs to be stopped immediately after the steel ball reached the ground because the timing might not accurate and this will affect the calculation as a result a wrong value of gravity will be obtained.

CONCLUSION

From the experiment, it can be concluded that the acceleration of the steel ball is affected by the gravity which is 9.8 m/s2, but we did not obtain the precise value of the gravity because based from the data and calculation had been made our acceleration due to gravity is 8.4 m/s2. Also, the mass of the steel ball was kept constant thus it did not affect the acceleration. We also know that the relationship between the acceleration and the different height of the ball released from the curved railing, which are directly proportional to each other. We found this by increasing the height in each experiment and timing each run to see if the time it took for the ball to roll down the curved railing is shorter, which it was. In other words, the higher the height of the ball released, the faster the acceleration, and the closer it gets to 9.8 m/s2. Overall, while we were not entirely accurate with our hypotheses, we completed our objectives, and learned from both our results and our mistakes.

REFERENCE

Sources

Book:

Fendt, Walter. “Projectile motion.” 9/13/200, 8/30/2006 http://www.walter-fendt.de/ph11e/projectile.htm

Internet:

https://podcast.punxsy.k12.pa.us/groups/laineyswiki/ revisions/1aeda/17/

http://honorsphysicsrocks.wikispaces.com/