Investigating the Trajectory of a Small Ball as it Rolls Off a Surface Which is Inclined to the Horizontal

FHSC1014 Mechanics

FOUNDATION IN SCIENCE

PRACTICAL:
Practical 3
TITLE:
To investigate the trajectory of a small ball as it rolls off a surface which is inclined to the horizontal
DATE:
25/6/2014
NAME:
Yeoh Boon Khai
ID:
1403449
GROUP:
P8
LECTURER’S NAME:
Mr Zoheir

Title:

Objective: To investigate the trajectory of a two dimensional motion.
Apparatus and Materials:
1. Ramp
2. Wooden block
3. Pendulum bob
4. Plumb line
5. Steel ball
6. Wooden board
7. Carbon paper
8. Meter rule
9. Plasticine

Figure 4-1

Setup:
2. A ramp has been set up at the edge of a bench as shown in the Figure 4-1.
3. Suspend a plum-line from the edge of the bench as shown in Figure 4-2.
4. Mount a wooden board horizontally using two clamps so that the board is situated about the bottom of the ramp.
5. Place a sheet of blank paper on top of the board.
6. Place a piece of carbon paper on the top of the blank paper. The ink-side of the carbon paper should be facing down.
7. When a ball is released at the top of the ramp, the ball will travel through a trajectory as shown in Figure 4-2.

Figure 4-2
Theory:

Let:

g = 9.8 ms-2 u = speed of the ball as it leaves the ramp k = constant y = vertical distance (between the bottom of the ramp and the top of the board) x = horizontal distance (between the plum-line and mark on the paper)

The equation which relates x and y is

Procedure:
1. The ball is positioned at the top of the ramp. The ball is released so that it rolls down the ramp and onto the board below.
2. The carbon paper removed and observes that the ball makes a small mark on the blank paper.
3. The vertical distance y and the horizontal distance x is measure and record.
4. The value of y is reduce and repeat the steps above to obtain eight (5) sets of values of x and y.
5. y, x, and y/x is tabulated. 6. A graph of y/x against x is plotted.
7. The gradient and y- intercept of the graph is determine.
8. The answer is used from [7] to determine values of k and u.

Observation
Data from experiment
X(cm)
Y(cm) y/x 22.2±0.1
30.0±0.1
1.35
25.5±0.1
40.0±0.1
1.57
29.5±0.1
50.0±0.1
1.69
32.0±0.1
60.0±0.1
1.88
34.5±0.1
70.0±0.1
2.04

Graph y/x against x
Calculation:

k= y-intercept = 0.1615

=0.0537

=2u2

=2u2

2u2=187

u=9.67ms-1

Discussion
[According to Ideal projectile motion states that there is no air resistance and no change in gravitational acceleration. This assumption simplifies the mathematics greatly, and is a close approximation of actual projectile motion in cases where the distances travelled are small.]1. [The positive x-direction is horizontal and to the right, and the y-direction is vertical and positive upward. The most important experimental fact about projectile motion in two dimensions is that the horizontal and vertical motions are completely independent of each other. This means that motion in one direction has no effect on motion in the other direction.]2

[ A projectile is any object that has been thrown, shot, or launched, and ballistics is the study of projectile motion. Examples of projectiles range from a golf ball in flight, to a curve ball thrown by a baseball pitcher to a rocket fired into space. The flight paths of all projectiles are affected by two factors: gravity and, on Earth at least, air resistance]3

Base on this experiment ,we assume that the gravitation force is a positive value which is pointing downward. Beside, according to the collected data and the plotted graph it is obviously that the longer the Y (cm) the longer the X (cm) which the Y/X is linearly proportional to the X (cm). However, this experiment has some mistake due to human factor. For example, the ball may not place at the same spot each time during the experiment. During experiment, some precaution we should take to gain the actual result. For example we must make sure that the position of stand with wooden board is only change in the height of it but never moved the angel between the table and the wooden block. During experiment, we make sure the position let the ball rolling down is always same.

Reference
1) http://en.wikipedia.org/wiki/Range_of_a_projectile#Ideal_projectile_motion
2) Serway, R.A. & Vuille, C. (2012).College physics.(9th ed.). Belmont, CA: Cengage Learning Brooks/Cole.
3) http://www.scienceclarified.com/everyday/Real-Life-Chemistry-Vol-3-Physics-Vol-1/Projectile-Motion.html#ixzz368O9fm5p

Conclusion
When change the input variable, the height the ball is from the ground, the distance the ball rolls will be proportional to that change. As increase the height of the ball from the ground, the distance it rolls will increase.