Physics Lab 3 Complete

PHYS 211
Physics for Science and Engineering

Experiment 1: Projectile Motion
Physics Lab Report 3

OBJECTIVE
The objective of the experiment is to measure the speed at which a projectile leaves a spring gun and to predict the landing point when the projectile is fired at a nonzero angle of elevation.

EQUIPMENT
Spring gun

Metal ball

Protractor

Meter stick

Ruler

Whiteboard markers

THEORY
Projectile motion is an example of motion with a constant acceleration. In this experiment, a projectile will be fired from some height above the floor and the position where it lands will be predicted. To make this prediction, one needs to know how to describe the motion of projectile using the laws of physics. The position as a function of time is:
(1)
By measuring the appropriate quantities, one can predict where the projectile will strike the floor. Eq. (1) is a general form describing the position of an object. It can be resolved into x and y components as:
(2)
and
(3)
Which will give the position of the projectile in the x and y directions. The x and y components of the initial velocity are (Fig. 4.2)
(4) and
For a projectile, there is no horizontal acceleration after the gun is fired. The inly acceleration is due to the gravitational attraction of the Earth. This acceleration has a negative Vertis direction (Fig. 4.2). Hence, the Eqs. (2) and (3) become
(5) and
These equations of motions describe the motion of a projectile.

Figure 4.2 Projectile motion. The Trajectory is a parabola.

PROCEDURE
1. Record the number inscribed on the firing mechanism of the pendulum. You will need it for a future experiment.
2. Place the ballistic pendulum on a platform with the pendulum arm in the up position. Measure the height from the bottom of the ball as follows: Use the height gauge to measure distance from the table top to the bottom of the ball and the meter stick to measure the height of the table above the floor. Add these two distances together to get the total height h.
3. Calculate the amount of time the ball will be in the air when fired horizontally, recall that if two balls are released at the same time, one falling vertically and the other projected horizontally, both will hit the ground at the same time.
4. Video instructions can be found on your computer. Fire the spring gun from the 1st detent, being sure to hold the gun firmly in position. (Also, make sure that no one is in the flight path!) Note where the ball lands. Color the ball with whiteboard marker so that it can mark the floor when it lands. Fire the spring gun 5 times.
5. For each trial, measure the total distance the ball traveled horizontally. (Be sure to measure the total distance from the pendulum in the uncocked position to the point of impact on the floor.) Find the average horizontal distance of all the trials. From this value and the time calculated in step 3, calculate the speed at which the ball leaves the gun.
6. Tilt the spring gun backwards and measure and record the angle of elevation. Measure the distance from the bottom of the ball to the floor.
7. Using Eqs. 4&5 and the quadratic equation calculate the horizontal range of the ball when fired at the above angle and height in step 6.
8. Mark the floor at eh location the ball is calculated to land. Place the line on the target at this location, fire the ball at the target three times and determine the average distance, calculate the percentage difference between the R and the average measured range. If the distance calculated and the distance obtained from firing the gun are substantially different, check your calculations. Fire the gun again after locating and correcting your errors.

CALCULATIONS
(i) The ball is launched horizontally
The distance travelled in the five repeated experiment
Let Sx = distance (range) travelled by the ball horizontally S1 = 139.1 cm S2 = 138.9 cm S3 = 136.4 cm S4 = 138.2 cm S5 = 129.3 cm
Average distance travelled by the ball = (S1 + S2 + S3 + S4 + S5) ÷ 5 = (139.1 cm + 138.9 cm + 136.4 cm + 138.2 cm + 129.3 cm) ÷ 5 = (681.9 cm) ÷ 5 = 136.38 cm = 1.364 m
Let Sy = height in which the ball is launched (vertical height) = 93.5 cm = 0.935 m
Note: - Horizontal acceleration, ax = 0 m s-2
Vertical acceleration, ay = 9.81 m s-2
The time taken for the ball to reach the ground Sy = uyt + ½ at2 -0.935 m = ½ (-9.81) t2 T = 0.437 s
The initial horizontal velocity of the ball is calculated using the formula. Sx = uxt + ½ at2 1.364 m = ux ( 0.437) + 0 ux = 3.12 m s-1

(ii) The ball is launched at an angle of 30 degree
The distance travelled by the ball in the five repeated experiment
Let Sx = distance (range) travelled by the ball horizontally S1 = 161.9 cm S2 = 156.8 cm S3 = 158.5 cm S4 = 161.0 cm S5 = 158.9 cm

Average distance travelled by the ball = (S1 + S2 + S3 + S4 + S5) ÷ 5 = (161.9 cm + 156.8 cm + 158.5 cm + 161.0 cm + 158.9 cm) ÷ 5 = (797.1 cm) ÷ 5 = 159.42 cm = 1.5942 m
Let Sy = height in which the ball is launched (vertical height) = 93.5 cm = 0.935 m
Note: - Horizontal acceleration, ax = 0 m s-2
Vertical acceleration, ay = 9.81 m s-2
Horizontal velocity, vx = 3.12 cos 30 = 2.70 m s-1
Vertical velocity, vy = 3.12 sin 30 = 1.56 m s-1
The time taken for the ball to reach the ground Sy = uyt + ½ at2 -0.935 m = 1.56 (t) + ½ (-9.81) t2 4.905 t2 – 1.56 t – 0.935 = 0 T = 0.624s or -0.306s
Thus, the time taken for the ball to reach the ground is 0.624 s The horizontal distance travelled by the ball: Sx = uxt + ½ at2 = 2.70 (0.624) + 0 =1.6848 m
Percentage error = (1.6848 m – 1.5942m) X 100% = 5.38 % 1.6848

DISCUSSION
In this experiment, we have learnt to use the spring gun and kinematic formulas to determine the initial velocity of an object in projectile motion.
The initial velocity of the metal ball in this experiment signifies the force exerted on the metal ball. Since the force acting on the metal ball is set to be the same for both projectile motion with and without motion, the initial velocity for both experiment would be the same. Plus, we assume the only acceleration exists in the experiment is gravitational force. Hence, horizontal acceleration does not exist. The theoretical range of the projectile motion with angle can be determined using the following formula:
Sx = uxt + ½ axt2
Since ax = 0 ,
Sx = uxt
Based on the calculation, the percent error in the experimental value of range, Sx is 5.38%. The experimental value is slightly smaller than the theoretical value. This is due to the air resistance in the air.
Air resistance in the air is a random error in this experiment as we can’t predict the motion of the air particles. Hence, to get a more accurate result, the metal ball is fired 5 times for each experiment and the average range value is calculated.
As precaution steps in this experiment, the experiment is carried out indoor to reduce the error in the experiment. The unpredictable wind outdoor would simply alter the resultant range in this experiment. Besides, the same metal ball is used throughout the experiment to ensure the same production of force in the experiment. Also, the spring gun is firmly positioned to the degree of projection to ensure the accuracy in calculation of result. While the spring gun is adjusted to certain degree, the scale on the spring gun is read with eye-level perpendicular to the scale to avoid parallax error. Last but not least, for safety, we ensure that nobody is in the flight path before firing the metal ball.
In this experiment, we have applied Galileo’s Law of Projectile in our calculation. This law states that a horizontal motion will move at a constant motion in the absence of external force and a falling body would accelerate downwards at a constant rate neglecting air resistance and friction. In this experiment, we assume the metal ball is moving downwards under a constant gravitational force and moving horizontally at a constant velocity. Not only that, we applied the Associative Law of Vector Addition in this experiment. This law states that the sum of vectors remains same irrespective of their order or grouping in which they are arranged. In this experiment, the calculation for horizontal components (x- component) and vertical component (y-component) is separated. This law is verified with the small percent error in calculation of the range.

QUESTIONS

1. Comment on the following statement: “When a bullet leaves the barrel of a gun, it doesn’t drop at all for the first 100 meters of flight.” Is this statement true or false? Explain.

The statement is false because the moment when the bullet leaves the barrel of the gun, it experiences a downward acceleration due to the gravitational force. A projectile motion occurs when a body is only influenced by the downward force of gravity (provided that the air resistance is negligible).
According to the Newton’s First Law (also known as the Law of Inertia), a body in motion stays in motion with a constant speed and direction unless acted upon an unbalanced force. All objects on earth experiences a force of the gravity that is directed towards the center of the earth. This unbalanced force due to gravity will cause the bullet to drop. When the bullet leaves the barrel, the gravitation of the earth will cause the bullet to have a downward acceleration of -9.8 . Therefore, even if the bullet leaves the barrel at a high velocity, it will still experience a drop for the first 100 meters of flight.
2. What is the acceleration of a projectile fired vertically upwards? What is the acceleration fired vertically downwards?

The acceleration of a projectile is the same in both situations. A projectile is an object upon which the only force acting on it is the gravity. On earth, the gravitational force will cause the body to have a downward acceleration of -9.8 .
3. If the ball had twice the mass, but left the spring gun at the same speed, what effect would this have on its distance of flight? Neglect air resistance. Explain.

In projection motion, the mass of the ball does not affect the distance of the flight. Galileo discovered that all objects regardless of mass fall at the same rate in the absence of air resistance. This is because the inertial mass , which appears in is equal to the gravitational mass , which appears in the Newton’s universal law of gravitational equation . The and cancel each other in the equation. Thus, the mass does not affect the distance of flight.

4. In Fig. 4-2, suppose is constant and is varied. Is the angle that maximizes the range R equal to, less than, or greater than ?

The formula to get the range R of a projectile motion is . , The maximum value of is 1.
The range R is maximum when = 1.

.

Thus, the angle that gives that maximum range R is .

CONCLUSION
This lab taught the concepts of projectile motion. It taught that horizontal motion and vertical motion are independent of each other except for time. Using this common factor of time allows for the calculation of many different values. The lab also taught how to use the kinematic equations for two dimension motion, especially when the motion has a velocity at an angle.

ACKNOWLEDGEMENT
Name
Contribution
Shuhaib
Questions and Answers
Kar Men
Data Tabulation, Calculation and Analysis

Bing Yu
Discussion
Rui Qiong
Objective, Theory, Apparatus, Procedure
Harvinder Singh
Cover, Conclusion, Acknowledgement, Editing