Projectile Motion

Object of Experiment: During this lab, we used the kinematic equations in both the horizontal and vertical directions in order to measure the velocity of a ball from a projectile launcher and predict where the ball would land when the launcher was launched at an angle. We then measured the distance of the ball when launched at an angle to compare to our theoretical prediction.

Equipment:

Projectile Launchers

Ramrods

Steel Ball

Meter stick

Small C clamp

White paper and carbon paper

Plumb bob

Tape

Principles:

Projectile motion occurs when an object is launched into the air and the only acceleration acting on the object is the acceleration due to gravity in the vertical direction. Therefore, there is no acceleration in the horizontal direction and the vertical and horizontal motions are independent of each other. Projectile motion results in a parabolic path for the object through the air. Pure parabolic projectile motion assumes there is no air resistance acting on the object as it travels through the air.

Because the motions in the horizontal and vertical directions are independent of each other, the kinematic equations can be used separately in each direction.  In the horizontal direction, the displacement of the object is given by:

       (1)

where v0x is the initial velocity in the x direction and t in the amount of time the object in in the air. The amount of time the object is in the air is dependent on the motion in the vertical, y, direction. The displacement in the y direction is given by:

     (2)

where v0y is the initial velocity in the y direction and g is the acceleration due to gravity on Earth which is equal to -9.8m/s2.

Figure 1

           If a projectile is fired in the completely vertical direction, then the initial velocity, v0, is equal to the initial velocity in the x direction, v0x. This concept can be used to find the initial velocity of a launcher. By measuring the height of the launcher, ?y can be found. Then, from equation 2, the time that the object is in the air can be calculated since it is known that the initial velocity in the y direction is zero when fired horizontally. Once the time is known, the initial velocity of the launcher can be found by experimentally determining ?x, the displacement in the horizontal direction, by firing the projectile and measuring how far away it lands in the horizontal direction.

           Once the initial velocity of the launcher is known, the range, or displacement in the x direction can be predicted for any launch angle, ?. For a given angle, ?, the components of the initial velocity can be found using trigonometric functions as follows:

     (3)

Once the components of the initial velocity are known, equation 2 from above will give the time of flight and then equation 1 will give the predicted range for the projectile.

Figure 2

Procedure:

Measure the height of the launcher to determine how long the projectile is in the air when launched horizontally.

With a launch angel of 0, fire the projectile several times in order to measure the displacement in the x direction from the center of the spread and estimate the uncertainty using the spread in range from multiple launches.

Calculate the initial velocity from the time and displacement in the x direction.

From an assigned launch angle, calculate the components of the initial velocity.

Compute the expected flight time and expected range as well as a maximum and minimum value for the range based on the percent spread form above.

Fire the projectile at the given angle, measure the range, and compare to the calculated value.

Data

Table 1: For horizontal launch

Parameter

Value

?y  measured

1.12 meters

t calculated

0.48 seconds

?x measured to center of spread

1.87 meters

Spread of ?x measured

4 cm

%spread of range calculated

2.1%

v0 calculated

3.90 m/s

Table 2: For launch angle of 40 degrees

Parameter

Value

v0x  calculated

2.99 m/s

v0y  calculated

2.51 m/s

t calculate

0.80 seconds

x calculated

2.38 meters

x(min) and x(max) calculated

2.33 – 2.43 meters

x measured

2.31 meters

Conclusions:

Our percent error between our measured range on 2.31m and our expected range of 2.38m is 2.9% which is just slightly higher than the 2.1% error that could be expected from the spread in the range when the launcher was fired horizontally. One possible explanation is that air resistance affected our projectile. This is likely since our projectile fell short of our expected range and air resistance would cause this as it would slow down the projectile. Another source of error is the uncertainty in the angle measurement. We were only able to set our angle to within about 1 degree and this uncertainty was not taken into account when calculating the minimum and maximum expected range. Even with our slightly larger than expected percent error, we were able to hit the target which shows that the kinematic equations can be used to predict where a projectile will land.

PHYS 2425/2426

Lab Report Rubric

100 points on each lab report

Use 12 pt. font and double spacing.

The lab report will have the following parts:

(5 points) Heading ? With group members names, date of the experiment, and title of the experiment.

(10 points) Abstract? State the purpose of the experiment, what was the experiment testing or trying to prove, etc., and how it was tested. Use 1-3 complete sentences.

(5 points) Equipment ? Provide a list of the equipment used, a bulleted list is appropriate.

(30 points) Principles ? Explain the scientific principles, theories, and physical laws involved in the lab. Define any terms, justify any assumptions, provide and explain the equations used, and provide any useful figures. This section should be done in complete sentences and around 3-5 full paragraphs. It should be a good summary of the respected section in your textbook.

(5 points) Procedure ? Briefly state the steps you took to complete the experiment. This should include enough information so that another student could also complete the experiment.

(25 points) Data ? Include all the data acquired through the experiment. Present the data with data tables and graphs. Explain what the data means and show all relevant calculations. Make sure to include units and the proper labels and axis.

(20 points) Conclusion ? Provide a summary based on the analysis of your data. What does the data suggest, what are the trends, etc.? Does this fit with the current theory? Where you correct in making the assumptions? Make comparisons if possible. Include sources of uncertainty within your measurements.