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Lab – Bull’s Eye

 

 

Purpose

 

To investigate the independence of horizontal and vertical components of motion.  To predict the landing point of a projectile.

 

Required Equipment/Supplies

 

Ramp

˝” (or larger) steel ball

small cup

meterstick

plumb line

stopwatch or

            Photogate

            TI 83+ w/ Datagate pgrm

           

 

Discussion

 

An object that is 5 m above the ground will take one second to fall to earth when dropped.   And an object 5m above the ground will take the same time to fall even if it is launched or thrown horizontally.  In today’s lab you will calculate the speed of a marble coming off the ramp and the time of decent based on the height of your lab table.  With these two measurements you can accurately predict where the marble will hit the floor when allowed to roll down the ramp and off the table.  Good luck!

 

 

 

 

 

Procedure

 

Step 1 (compute the horizontal speed):  Assemble your ramp.  Make it as sturdy as possible so the steel balls roll smoothly and reproducibly.  The ramp should not sway or bend.  The ball must leave the table horizontally.  Make the horizontal part of the ramp at least 20 cm long.  The vertical height of the ramp should be at least 30 cm.

 

 

 

 

 

Step 2 (compute the horizontal speed):  Use a stopwatch or photogate to measure the time it takes the ball to travel from the first moment it reaches the level of the table top to the time it leaves the table top Divide this time interval into the horizontal distance on the ramp to find the horizontal speed.  Release the ball from the same point (marked with tape) on the ramp for each of three runs.

 

Do not permit the ball to strike the floor!  Record the average horizontal speed of the three runs.

 

                                    Horizontal speed =                                          

 

Step 3 (measure the vertical distance):  Using a plumb line and a string, mesure the vertical distance h the ball must drop from the bottom end of the ramp in order to land in an empty soup can on the floor.

 

1.         Should the height of the can be taken into account when measuring the vertical distance h?  If so, make your measurements accordingly.

 

                        h =                                          

 

Step 4:  Using the appropriate equation from the discussion, find the time t it takes the ball to fall from the bottom end of the ramp and land in the can.  Wright the equation that relates h and t.

 

                                    Equation for vertical distance: =                                           

 

Show your work in the following space.

 

 

 

 

 

 

 

Step 5 (predict the range):  The range is the horizontal distance of travel for a projectile.  Predict the range of the ball.  Write the equation you used and your predicted range.

 

                                    Equation for range: =                                                   

 

                                    Predicted range d: =                                                   

 

Place the can on the floor where you predict it will catch the ball.

 

Step 6 (test your prediction):  After I have checked your predicted range and your can placement, release the ball from the marked point on the ramp.  See whther the ball lands in the can. 

 

 

Analysis

 

2.         Compare the actual range of the ball with your predicted range.  Compute the percentage error.  (We’ll discuss the formula)

 

3.         What may cause the ball to miss the target?

 

4.         You probably noticed that the range of the ball increased in direct proportion to the speed at which it left the ramp.  The speed depends on the release point of the ball on the ramp.  What role do you think air resistance had in this experiment?