Return to Physics IndexProjectile Motion (or You Bet Your Grade)

Roy Coleman Morgan Park High School

1744 W. Pryor Ave.

Chicago, Illinois 60643

312-881-5050Objectives:

To calculate the initial velocity of a spring stretched a varying amount and

fired vertically from a shooter and to predict, by calculations, where that

spring will land when it is shot horizontally off of a horizontal platform. As

a additional objective, to learn that ALL data must be recorded but that data

which is way out of the ordinary can be ignored when calculating averages and

results.Materials Needed:

The following materials are needed for each group of 2-4 students:

1) a spring with sufficient elasticity so that stretching it about 1 cm will

shoot it to a height of about 50 cm. One end should have a paper clip

attached and the other should be bent into a loop which will hook over the

nail in the end of the shooter described below (Primary level students

might use rubberbands instead but they are not as consistent.)

2) a 'shooter' made from a 1" by 1" by 18" piece of wood with a headless nail

driven into the end near the edge so that the spring may be hooked to it

3) several metersticks

4) graph paper

5) a section of a room with sufficient height where a spring's shot may be

marked and/or measured directly

6) optional - an apparatus which simultaneously drops one object while

projecting a similar object horizontally

One of each of the following is needed for the entire class:

1) a securely mounted horizontal surface at a height of 1.5-2 meters above the

floor where the students will hold their 'shooters' for theYou Bet YourGradepart of the experiment

2) a low waste paper basketStrategy:

INSTRUCTORS PREPARATION:

1) Mark the 'relaxed' position of the spring on the side of the shooter.

2) Stretch and shoot the spring vertically such that it goes to a height of

about 50 cm. Make enough shots so that you are confident of the measurements.

Mark this stretch on the side of the shooter and number it #1.

3) Stretch and shoot the spring so that it goes to the greatest height that you

are going to use. Again, make enough shots so that you are confident of the

measurements. Mark this stretch on the side of the shooter and number it #6.

4) Measure the distance between the two marks (#1 and #6) and divide it by 5.

Measure down from #1 a distance equal to the result and mark that point #2.

Repeat the measurement for points #3 and #5, intentionally skipping where #4

should be. (A suggestion was made to drill holes at each of these points to

allow a small nail to be inserted and the paper clip hooked on the nail.

Pulling the nail fires the spring.)

CLASS ACTIVITIES:

1) Have the students fire the spring vertically from each of the indicated

stretches. They should record ALL of their data and decide which of the points

are consistent and which are in error. (Does the height get more consistent as

the student gets more experience?) (Does it make a difference if a different

person does the shooting?)

2) Plot a graph of height vs. stretch. (Is this graph a straight line?) (Does

it go through zero?)3) Calculate the initial velocity of the spring (v_{o}=sqrt(2gh)) for each of the

stretches and plot a graph of the initial velocity vs. stretch. (Is this graph

a straight line?)

4) Demonstrate that a projectile fired horizontally will take the same amount of

time to reach the ground regardless of its initial horizontal velocity. This

should demonstrate that the vertical acceleration of an object is independent of

the horizontal acceleration with the resulting motion being the sum of the two.

5) Show the students the board you have mounted horizontally and how their

shooter should be placed. Also show them the waste paper basket that they will

be shooting into.

6) Have the students predict, from their graphs, the initial velocity of their

spring for a stretch equal to what would be #4.

7) Have the students calculate the time that it will take forthe spring to

fall from the board to the top of the waste paper basket. (t=sqrt((2H)/g)) For a

high school class, you might just tell them to calculate the time to fall and

let them figure out that the spring doesn't fall to the floor but only to the

top of the basket.

8) The students should then calculate where to place the basket. (R=v_{o}t)

9) Place the center of the basket at the calculated place and have them try

shooting. (Did they hit it and how many tries did it take?)Expected Results:

The results for the first few shots should be somewhat inconsistent but,

after 5-10 shots, they should improve greatly. Generally the shots should group

within about 10% of the average value for each stretch.

Changing the person doing the shooting usually makes a noticeable difference

because each person has their own unique way of releasing the spring. Using a

shooter with holes and a nail release along the side should eliminate this

difference.

The graph of height vs. stretch should, with the possible exception of the

first point, be a straight line. It will probably not go through zero since a

spring is linear only from the point where all of the coils are separated and it

usually takes some small initial stretch to completely separate all of the

coils.

The graph of velocity vs. stretch shouldNOTbe a straight line because of

the square root used to calculate it but, for the small sample of points tested,

it will probably be very close to a straight line.Evaluation:

A student's grade is based on how many shots it takes for the spring to land

in the basket. (First shot = A, Second shot = B, etc.)