Physics 1

Experimental Tutorials

Week 4-8

Projectile Motion

Please complete the tutorial in your lab-book

Pre-lab Tutorial Question

A ball of mass m is placed at the start position on the track shown in figure 1, and allowed to roll along the track, falling a distance h vertically.

B.1 What is the ball’s kinetic energy as it leaves the track?

B.2 What is the ball’s velocity as it leaves the track?

(Hint: What is its change in potential energy?)

B.3 The end of the track is set along the horizontal. Find an expression for how long it takes the ball before it hits the landing pad a distance y below the launch point.

B.4 Find an expression for how far horizontally from the launch point it travels. Write your answer in terms of y and h.

Experiment: Projectile Motion

Learning Outcomes

 To study projectile motion.

 To analyse experimental data using Excel.

Part 1: Excel Spreadsheet

 Using Internet Explorer, navigate to the Physics 1 Moodle website. In the laboratory section you will find an Excel spreadsheet "Projectile Motion". Download this to your PC.

 Cells C5, C6 and C7 contain the equations you derived in the tutorial question for this experiment. They currently refer to empty cells, hence their current values.

 Measure the depth, y , from the launch point to the landing pad using an initial launch height, h , of 20 cm. Assume that g is 9.8 ms-2. Use the spreadsheet to …

1.1 Predict the launch velocity.

1.2 Predict the time of flight.

1.3 Predict the horizontal distance travelled after launch.

Part 2: Taking Data

 Set up the target at a distance so that the ball will hit the central zone of the target.

 Open the EasySense software package. You are interested in measuring the times of the ball passing through the light gates and hitting the landing pad.

 From the opening menu select: timing, raw times, next, at A or B, then finish.

 If you are unable to select raw times click the Level icon in the tool bar until 3 blue rectangles appear.

 Now from the Display option at top select Show Table – this will display the times recorded.

 The light gate is open until the ball travels through it; this closes the light gate by obstructing the beam in the light gate. You can now start the experiment using the start button. Release the ball and click stop once the ball has landed.

 You are only interested in the first 3 measurements although the computer might attempt taking 1000! (The other readings are from oscillations in the system, such as the target vibrating.)

(i) The first time recorded is when the ball enters the light gate.

(ii) The second time recorded is when the ball leaves the light gate.

(iii) The third time recorded is that of the ball hitting the landing pad.

 Enter these times into an Excel spreadsheet. Alternatively you can transfer the data into an Excel spreadsheet using the EasySense software itself: click File then Transfer to Excel.

 Once you have transferred the data from your first run, delete this data from the EasySense table. To do this you will need to highlight every cell by clicking on the top cell, holding shift, and clicking the bottom cell. Now click delete on the top toolbar to clear the cells.

 Repeat the experiment until you have carried it out three times.

2.1 Determine the actual launch velocity, time of flight and horizontal distance travelled for each of the three runs.

2.2 What do you think would happen to the launch velocity and flight time if you changed the release height, h? Perform. the experiment again with a different value for h.

2.3 Comment on the comparison between your results and predictions. What effects have you neglected in your analysis?

Add a printout of your excel spreadsheet to your lab book.

Hints:

a) You can use the spreadsheet you downloaded from Moodle for the calculations.

b) Measure the horizontal distance with a ruler.

c) You will need to measure the diameter of the ball to calculate the launch velocity.

d) Delete the data after each run. This will save you from having to restart the software each time.

Part 3: Launching at an angle to the horizontal

3.1 Derive the expression for the flight time and the distance travelled by the ball if it is launched at an angle θ to the horizontal and falls through a distance y - express your results in terms of θ, y and the velocity v.

3.2 Deduce the optimum launch angle that will produce the largest possible horizontal distance travelled. Hence comment on how the launch angle changes as (i) y tends to zero and as (ii) y tends to infinity.