Bowling Ball Lab



Dart Gun Muzzle Velocity

Your job is to determine the muzzle velocity of a dart gun.

Using only the equipment listed below,

you will develop three different methods to accomplish this goal.

(There are at least eight ways to determine the muzzle velocity with this equipment!)

❑ meter stick

❑ 10 meters of string

❑ tape

❑ pencil

❑ protractor

❑ stopwatch

❑ paper

❑ calculator

In the spaces provided below and on the next page you will:

1. Write a brief but concise procedure. Describe any measurements you will make and assign each a symbol.

2. Draw a simple but accurate diagram of your experiment. Label all measurements on your diagram with the appropriate symbol.

3. Show explicitly using equations how the measurements will be used to determine the muzzle velocity.

Solution Method #1

Solution Method #2

Solution Method #3

What could be done to eliminate errors and make your calculated velocity more accurate?

Which of your methods gives the most accurate muzzle velocity? Explain.

Key of sorts…

 

Vertical Launch methods:

1) Launch it vertical and measure the max height. Use v2 = v02 +2g(x - x0) with v at top = 0 and x = h. You can solve this one for either the ascending part of descending part of the trajectory.

 

2) Launch it vertical and measure the max height. Use v2 = v02 +2g(x - x0) and the fact that v launch = v land and both x and x0 = 0. Be careful of the signs on this one.

 

3) Launch vertical and time the flight to the top. Use v = v0 + gt with v at the top = 0. Be careful of the signs.

 

4) Launch vertical and time total time aloft. Use v = v0 + gt with v launch = -v land. 

5) Launch vertical and measure both max height and time to the top. Use x = x0 + v0t + ½gt2 with x0 = 0 and x = h. Be careful of the signs on g and v0.

 

6) Launch vertical and measure both max height and total time aloft. Use x = x0 + v0t + ½gt2 with x0 and x = 0. Be careful of the signs on g and v0.

 

Horizontal launch methods:

7) Launch horizontal and measure the height of launch and the landing distance. Use t = SQR(2h/g) and distance to solve.

 

8) Launch horizontal and measure the time of flight and the landing distance. Use v = x/t to solve.

 

 Angled launch "Range" methods:

9) Launch at angle and land at same height. Measure angle and Range. Use Range Equation.

 

10) Launch at angle and land at same height. Measure Range and time. Use Range/t and trig to find vx. Work backwards with trig to find v.

 

Angles Launch with landing at different height then the launch height.

This is the hardest method... There are multiple methods for solving this one. In each case you need to measure launch angle, landing Range and either difference between launch and land height or the time of flight. I suspect there are at least a ½ dozen ways to do this one but... If students pick this method it is important to coach them on how to set up an effective and simple laboratory experiment. (Simple implies easier, cheaper, more repeatable, and less chance for error!) In fact it may be a good idea to cover that even if they don't pick this method...

 

Which methods are the best??

Generally speaking: If human measurement is involved... measuring distance is easier and more accurate. Human timing with a stop watch is prone to more errors unless the times are long enough to minimize reaction time. If electronic time measurement is available then the timing methods are great.

 

In any of the methods, the experiment must be repeated several time to minimize errors.

 

Special note: The launch speed of the dart will differ between vertical and horizontal launch! This is due to the spring having to work against gravity in the vertical scenario. The vertical muzzle velocity should be less the horizontal muzzle velocity. However... If you are using the cheap plastic dart guns... your students probably won't see much of a difference because the launch repeatability is so poor. :)

 

Hope that helps!

CB

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