This lesson is based on California's Middle School Integrated Model of NGSS.
MS-PS2 Motion and Stability: Forces and Interactions
PE: MS-PS2-2 - Plan an investigation to provide evidence that the change in an object's motion depends on the sum of the forces on the object and the mass of the object.
DCI: PS2.A: Forces and Motion: All positions of objects and the directions of forces and motions must be described in an arbitrary choose reference frame and arbitrary chosen units of size. In order to share information with other people, these choices must also be shared.
Science and Engineering Practices 3: Planning and Carrying Out Investigations - Collect data about the performance of a proposed object, tool, process or system under a range of conditions.
Crosscutting Concept: Systems and System Models - Create a small-scale artificial system isolating variables (distance and time) to calculate real-world measurements, such as velocity and acceleration.
This activity is designed as a lesson to use CPO's Car and Ramp kit, Physics Stand, and Timer with Photogates in order to calculate velocity. The eventual goal is to have your students calculate the acceleration of the moving car (Car and Ramp - Calculating Acceleration). It is recommended that students first practice with the equipment (Car and Ramp - Student Practice) before attempting to calculate velocity or acceleration. Additional practice may be needed in order to calculate velocity (Calculating Velocity Practice) and acceleration (Calculating Acceleration Practice).
The purpose of this lesson is to allow the students a chance to gather data, such as distance and time to calculate the velocity of the car on the ramp. The students will set the equipment up correctly, attach and activate the timer and photogates, role the car down the ramp, record the car's time through the photogates, and record the distance between the photogates. In doing so they have planned and executed an investigation that demonstrates that an object rolling down an incline will increase it's velocity and acceleration over time (MS-PS2-2). They will use descriptive labels such as centimeters and seconds to describe the distance between photogates and the time the car took to pass through specified photogates respectively (PS2.a). By collecting this sort of data they will be able to calculate velocity and and eventually acceleration under a range of conditions that include different positions along the ramp, changes in ramp angle, and mass of the car (SP3). By isolating the different variables on a ramp such as this the students can learn basic physics concepts that can be applied in the future to more complex real-world scenarios (CCC).
The order of instruction is as follows:
The following equipment are required for this activity:
The purpose of this particular activity is to calculate the velocity of the moving car on the ramp by measuring the distance between the two photogates and timing how long it takes to pass through the two photogates. By dividing distance by time the students are calculating the car's velocity in cm/s.
The students must be shown how to set-up the equipment.
The stand supports the ramp and the ramp holds the car and the timers with photogates. At the end of the ramp is a wooden foot that elevates the ramp above the ground. The photogates are the black clamps (seen in the above picture) that clamp onto the ramp along a printed ruler. The photogates create an invisible beam of light that is broken (to start the timer) when the car's wing passes through it.
The Timer is connected to the photogates and displays how long the car took (in seconds) to travel through the gates. For this activity two photogates are used. The top photogate (along the ramp) must be plugged into the 'A' input and the bottom photogate (along the ramp) must be plugged in the 'B' input in order for the timer to correctly time the car's passage along the ramp. Students must record the distance between photogates 'A' and 'B'.
TIP: I recommend that the students place the two photogates on whole numbers, such as 70cm and 20cm. This results in a distance of 50cm between the two photogates, which is a lot easier to use in calculations.
Weights are added to the car after each race to provide variation to the activity. The wing on the car breaks the invisible light beam on the photogates.
To make it easier to communicate desired ramp positions to my students I used a marker and numbered the holes on the stand from 1 to 19. When I want all my students to be testing at a specific angle I can tell them to place the ramp on the 'four hole' spot. FUNNY STORY - My eighth graders adopted 'four hole' as their new secret curse word and began using it at lunch. Several of the lunch proctors asked me what a 'four hole' was.
As part of the clean-up procedures the students are shown how to place the Timer equipment back inside the storage box, so as to not smash/break any of the equipment.
The students first position the ramp at the lowest setting possible to achieve the slowest speed, in this case the lowest setting is hole #4. The slower moving car gives them a better visualization of what they are doing. (This activity is designed to be experienced after Car and Ramp - Student Practice and before Car and Ramp - Calculating Acceleration.)
TIP: They will want to immediately place the ramp at the highest setting to get the greatest speed. I let them know that if they can be patient now, I will allow them to place the ramp at the highest setting during a later activity.
Once the ramp is in position, the students set up the timer and the photogates. Their two photogates need to be plugged into the 'A' and 'B' inputs (making sure the top most photogate is plugged into 'A' and the lower photogate 'B') and the timer needs to be set to 'Interval' so that it acts as a stopwatch when the car activates the gate.
The students experience a total of twelve races (one race = one timed roll down the ramp) and have the option of placing the gates at any position they desire. Four races are timed at the 4 hole, four races are timed at the 6 hole, and four races are timed at the 8 hole. The first race at each hole has no weights attached, the second race has one weight attached, the third race has two weights attached, and the fourth race has three weights attached. NOTE: The maximum weight limit is three weights and each weight weighs approximately five grams.
Once the two photogates are installed, I recommend students keep the gates at those locations for the duration of this activity. The distance between the two gates are the distance used in the velocity formula. I also suggest to students that they pick locations that yield a whole number. I tell them the ideal spot to place the 'A' gate is the 20 cm position and the 'B' gate at the 70 cm position in order to achieved a distance of 50 cm (much easier to calculate with).
The students are recording the time the car takes to go through the photogates (t) and the distance between the photogates (d) to calculate the velocity of the car (V) using the formula V=d/t.
Once students have their twelve velocity calculations, they graph their calculations with Double Photogate Lab - Velocity Graph and answer a set of questions.
Students are responsible for their own data collection (Double Photogate Lab - Velocity and Double Photogate Lab - Velocity Graph). They record the distance they placed the two photogates at and the time the car takes to pass through photogates 'A' and 'B'. Dividing these two values produces the velocity of the car under specific circumstances. All values must have the correct label in order to be counted as correct. The velocity values are then graphed and analyzed in order to answer a series of questions.