Lab #4: Projectile Motion of a Ball Fired from a Spring Gun

Lab #4: Projectile Motion of A Ball Fired from a Spring Gun

I. Analyzing and Predicting the Motion of a Ball Fired from a Spring Gun

In this exercise, you will examine the path of a projectile that is ejected from a spring gun. A) Initially, the projectile will be fired in the horizontal direction (see Figure 1). You will measure the initial height (yi) and the final range (xf) of the projectile and determine the time that it takes the projectile to fall and the initial velocity of the projectile. You will also use the minimum and maximum range to characterize the uncertainty in the velocity (difference between maximum and minimum) of the gun. B) Next, you will set the gun at an arbitrary angle to the horizontal (between 10 and 20 degrees). Using this angle and the velocity of the gun, you will predict the range (x2). You will test this prediction by firing the gun and measuring the range.

Part A 1. Set the spring gun so that it is horizontal and near the edge of the table. 2. Check that the spring gun platform is level to ensure that the projectile is being fired in the horizontal direction (Make sure that the ball does not role forward in the spring gun). 3. Carefully and cleverly mark a spot (with masking tape) on the floor directly below the point where the ball leaves the spring gun platform. Measure (to the nearest mm) and clearly record the initial height (to the bottom of the ball) of the projectile.

4. Fire a test shot and observe the location where the ball lands and tape a piece (or pieces) of paper to the floor at this location. 5. Fire five more shots and mark where they land on the paper (they should make small dents in the paper). 6. Using your best judgment, clearly mark a spot on the paper that represents the average range of these five shots. Measure the distance from the point below the spring gun platform to this spot (to the nearest mm). This is your measured range. Clearly record your value for the range. 7. Measure and record the distance between the shot that lands furthest from the gun and the shot that lands closest to the gun. This gives you the uncertainty in range, which later may be related to the uncertainty in the velocity of the gun. 8. As you would for a homework problem, draw a clear diagram showing the motion of the projectile and all known and unknown values. Using the kinematic equations, determine the time the projectile is in the air and the initial SPEED of the projectile. (Note, in this set up the initial horizontal velocity and initial speed of the object are the same because the gun is aimed horizontally.) Using the time the projectile is in the air and the uncertainty in the range, determine the uncertainty in the velocity of the gun (difference between minimum and maximum velocity).

Part B 1. Change the angle of the spring gun so that it is somewhere between 10 and 20 degrees above the horizontal. Measure and record this angle. 2. Carefully and cleverly mark a spot (with masking tape) on the floor directly below the point where the ball leaves the spring gun platform. Measure (to the nearest mm) and clearly record the initial height (to the bottom of the ball) of the projectile (yi). 3. As you would for a homework problem, draw a clear diagram showing the motion of the projectile and all known and unknown values. Using the height (yi), the speed obtained in part A, and the angle measured in step 1, calculate the time that the ball will be in the air and the range (xf) when it hits the ground. This is your predicted range. 4. Tape a piece of paper to the ground at the predicted range you obtained in step 3. Clearly mark your prediction on the paper and put an aluminum can at the spot. Call your instructor over before you fire your shot. Fire. How did you do? 5. Fire and mark five shots. Clearly mark a spot on the paper that represents the average range of these five shots. Measure and record the distance from the point below the spring gun platform to this spot (to the nearest mm). This is your measured range. 6. Calculate the percent difference between your measured and predicted range. %diff = 100 * |Xfm-Xfp| / ( (Xfm+Xfp)/2 ) Submit one page of recorded measurements and pertinent diagrams and calculations for part A and another for part B.

II. Angle of Maximum Distance 1. Please note the following applets are exceptionally good for getting to know projectile motion. The first two are highly recommended. http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/ProjectileMotion/jarapplet.html http://www.ngsir.netfirms.com/englishhtm/ThrowABall.htm http://jersey.uoregon.edu/vlab/Cannon/ http://www.phy.ntnu.edu.tw/java/projectile/projectile2.html http://www.geocities.com/thesciencefiles/projectiles/projectile.html

2. Create a table with the firing angle of the projectile and the corresponding horizontal distance traveled by the projectile. 3. For firing angles form 15 to 55 degrees, measure the horizontal distance traveled by the projectile. (BE CAREFUL WHEN FIRING!) 4. Make a graph with the horizontal distance on the y-axis and the angle on the x- axis. 5. Fit these data to a second order polynomial trendline. 6. Use the graph to determine the angle at which the maximum distance is achieved. 7. Submit the graph and explain why the maximum distance achieved does not occur at 45 degrees.

III. Shoot the Target Demo Your instructor will run a demo of a projectile fired at a falling ball. Draw a “strobe light diagram” to explain what you observe.