Java程序辅导

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.