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 acceleration. This lesson represent the culminating goal of having your students calculate the acceleration of the moving car, after hey first calculated the velocity (Car and Ramp - Calculating Velocity). 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 initial velocity, final velocity, and time between photogates to calculate the acceleration of the car on the ramp. The students set the equipment up correctly, attach and activate the timer and photogates, roll the car down the ramp, record the car's time through each 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 use descriptive labels such as seconds to describe the time the car took to pass through specified photogates and the time it took to pass between both photogates (PS2.a). By collecting this sort of data they will be able to experience acceleration in a range of conditions including different positions along the ramp, changes in ramp angle, and mass of the car (SP3). By isolating the different variables on a ramp 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 is required for this activity:
The purpose of this particular activity is to calculate the acceleration of the moving car on the ramp by calculating the car's speed through the top photogate 'A' and the bottom photogate 'B'. The time it takes for the car to pass through both photogates is also recorded. This lab can be confusing for the students if they do not have adequate experience with the equipment, thus the reason for a practice activity (Car and Ramp - Student Practice).
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 attach 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 takes (in seconds) to travel through the gates. For this activity only one gate is used. When only using one photogate, it must be plugged into the 'A' slot and the Timer must be set to 'Interval' (default setting). When the car passes through the 'A' gate the Timer displays seconds up to four decimal places. This is the value my students record for this activity.
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.
The timer does not calculate the velocity through photogates 'A' and 'B'. This must be done by the students. The timer does record the time through each photogate (similar to the data recorded in Car and Ramp - Student Practice). The time the car takes to pass through photogate 'A' is divided by the distance of the car's wing (distance) to calculate the car's velocity at that particular photogate. The car's wing measures 5 cm so the velocity formula uses a distance of 5 cm. Photogate 'A' would represent the initial velocity and photogate 'B' would represent the final velocity. Subtract the initial velocity 'A' from the final velocity 'B' and divide that value by time (A to B) to determine the car's acceleration in cm/s/s.
EXAMPLE: The car passes through photogate 'A' in .0568 seconds. This is divided into a distance of 5 cm to arrive at a velocity of 88.03 cm/s (rounded to the nearest hundredths) at the 'A' photogate. Repeat the same procedure for the 'B' photogate. If your students are using calculators, make sure they type in the 5 first (5 / .0568 = 88/028169). The most common error I see is flipping the calculation. We spend time talking about what a realistic velocity should be. The timer will also reveal the time the car took to go from 'A' to 'B'.
To calculate acceleration use the above example to calculate initial velocity 'A' time and final velocity 'B' time. Subtract final velocity from initial velocity and divide that value by the total time between 'A' and 'B'.
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 Car and Ramp - Calculating Velocity.
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. They will set up two photogates and they need to be plugged into the 'A' and 'B' input (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 car was a wing on one side that needs to face towards the photogate.
The students will experience a total of eight races (one race = one timed roll down the ramp). The students have the option of placing the gates at any position they desire. Four races will be timed at the 4 hole and four races will be timed at the 8 hole. The first race at each hole will have no weights attached, the second race will have one weight attached, the third race will have two weights attached, and the fourth race will have three weights attached. NOTE: The maximum weight limit is three weights and each weight weight approximately five grams.
Once the two photogates are installed I recommend that the students keep those gates at those locations for the duration of this activity. The actual distance between the two gates is immaterial for this activity as this value is not used in the acceleration formula.
The students will be recording the time the car took to go through each photogate and the time the car took to pass between photogate 'A' and 'B'. The acceleration formula subtracts the starting velocity 'A' (Vi) from the final velocity 'B' (Vf) and divides that by the time between photogates 'A' to 'B' (t).
To calculate initial velocity the students will need to use the velocity fromula (V=d/t). The 'A' photogate time (t) is divided by the distance of the car's wing of 5 cm (d). The same procedure is used for final velocity, except the students will use the 'B' photogate time. Once the two velocities have been subtracted (final velocity - initial velocity) it is divided by total time ('A' to 'B').
Each student is responsible for their own data sheet (Double Photogate Lab - Acceleration and Double Photgate Lab - Acceleration Graph). They have to accurately record their car's time while it passes through the 'A' photogate (initial velocity) and the 'B' photogate (final velocity). These two values have to be divided into distance, which is the length of the car's wing (5 cm) since the car's wing it what is activating and deactivating the timer as it breaks the invisible beam of light in the photogate. Dividing time into distance yields velocity. By subtracting the initial velocity 'A' from the final velocity 'B' and dividing that value by the total time through 'A' and 'B' that car's acceleration, in cm/s/s, is determined. All values must have the appropriate labels to be counted as correct.
Once the acceleration values have been computed, they are graphed and analyzed in order to answer a set of questions.