Acceleration on a Ramp
Based on AP Science Practices
How does the angle of incline affect a cart’s acceleration? Follow both sessions here and complete your printed lab report as you investigate.
Your work is saved on this browser. Keep your printed report as your main record.
Before you begin
Learning goal: Investigate how ramp angle affects acceleration, construct a quantitative graph, and use its slope to find an experimental value of g.
Have your printed lab report, calculator in degree mode, pencil and ruler ready. Write your name, date, class and lab partners on the report. This is an individual browser workspace; no login or online submission is required.
Success criteria & assessment
- Session 1: carry out a controlled investigation and calculate acceleration with units.
- Session 2: construct and interpret a graph, derive g from its slope and evaluate accuracy.
- Printed-report rubric: hypothesis, variables & method /4; data & calculations /6; graphing & analysis /6; evaluation & communication /4. Total /20.
Inquirer: ask testable questions, plan and test, and justify claims with evidence.
Collect data and calculate
A · Collect & calculate 25 min B · Explain 10 min C · Exit ticket 1 · 5 min
Part A · Explore, collect & calculate 25 min
On your printed report: select “Virtual ramp simulation” and write your hypothesis: “If the angle of the ramp increases, then the acceleration will … because …”.
Identify the independent variable (angle), dependent variable (acceleration) and controls: distance, same cart, release from rest and same ramp surface.
- Choose Δx before your first run and write it on your report. Keep it the same for the printed investigation; the control remains adjustable for exploration.
- Use angles 10°, 20° and 30°. Release from rest (vᵢ = 0); do not push.
- Record Δx, vᵢ and the photogate final speed vf in the matching row of your printed table.
- Calculate sin θ and acceleration yourself for every row. Sketch the apparatus and label θ, the release point, Δx and the photogate.
Collect for 15 minutes, then calculate for 10 minutes. The sensor includes ±1% simulated variation in final speed, so repeats can differ slightly.
Use 0 m/s for the printed lab; add a starting speed to explore.
0 = frictionless · 1 = high friction
Explore all four controls freely. For the printed investigation, keep Δx fixed, vᵢ = 0 and μₖ = 0.
Idealised sliding-friction model on the ramp and horizontal ground, joined by a smooth transition. Static friction is not modelled separately. Settings are adjustable between runs; no result is recorded if the cart stops before the photogate.
Measured results
Copy these measurements to your printed table. Calculate sin θ and a on paper; the site does not calculate or reveal them.
| Trial | Angle θ (°) | Δx (m) | vᵢ (m/s) | vf (m/s) | μₖ |
|---|
Part A · Calculate on your printed report
Use a = vf² − vi²2Δx. Include units and show your own working.
- A1: Show your working for sin θ at θ = 20°.
- A2: Show your full acceleration calculation at θ = 20°, with units.
- A3: What happens to a as θ doubles from 10° to 20°? Does a exactly double? Why or why not?
- A4: Would acceleration at 40° be larger or smaller than at 30°? Justify using your table.
Method reminder
Use degree mode for sin θ. For acceleration, square each velocity before subtracting, then divide by twice Δx. Keep extra digits until the final step.
Part B · Explain 10 min
Answer both questions in your printed lab report.
- B1: How does acceleration change as angle increases? Quote values from your own table.
- B2: Why must the cart start from rest and Δx remain constant? What would happen to your calculated a if the cart were pushed?
Part C · Exit ticket 5 min
Use the Exit Ticket tab for three multiple-choice questions and feedback. Record your score out of 3 on your printed report.
On paper: identify one question you got wrong and the correct method, then one thing you will check more carefully next time.
Before you leave
Graph and analyse
D · Graph 15 min E · Analysis 10 min F · Evaluation 10 min Exit ticket 2 · 3 min Reflection 2 min
Starter · Revisit your evidence
In your printed report: as sin θ increases, what happens to a? Predict the shape of a graph of a against sin θ.
View Session 1 measurements
Use your own sin θ and acceleration calculations from Session 1. The graph has numbered axes. Add your own data points and best-fit line.
Part D · Construct your graph 15 min
Plot a on the y-axis against sin θ on the x-axis. The horizontal scale runs from 0 to 1 in steps of 0.1; the vertical scale runs from 0 to 10 m/s² in steps of 1. Place each point yourself. You can edit the axis numbers if you need a different scale. No data points or best-fit line are supplied automatically.
Edit axis numbers
The 11 ticks are numbered for you. You may edit the labels: horizontal ticks run left to right and vertical ticks run bottom to top.
Click or tap the grid to place a point. For keyboard placement, use the grid-position fields below.
Place marks using the keyboard
These are grid positions, not measured values. 0 is the left/bottom edge and 10 is the right/top edge. Use your chosen scale to decide the location.
For a best-fit line, select the line tool and choose two positions along your proposed line. Do not join the dots. The site does not fit the line or calculate its slope.
Use the graph to complete Part D of your printed report. Copy it to the printed grid or attach your downloaded graph as your teacher directs.
On paper: is your graph a straight line? Does it pass close to (0, 0)? Circle an outlier if there is one.
Part E · Data analysis 10 min
Show your working and answer every question in your printed lab report.
- E1: Describe the relationship between a and sin θ. Is it linear? Does your line pass through (0, 0)? Justify using your graph.
- E2: Calculate the slope using two points on your best-fit line. This is your experimental value of g. Show the points chosen, rise, run and units.
- E3: Write your line equation in the form y = mx + b using a and sin θ. Identify the independent and dependent variables.
- E4: Use your equation to predict a at θ = 90°. What does that value represent physically?
Part F · Evaluation 10 min
Complete the evaluation on your printed report.
- F1: Calculate the percentage error of your experimental g using the accepted value 9.8 m/s². Show your working, then judge accuracy: below 5% very accurate; 5–10% reasonably accurate; above 10% low accuracy.
Percentage error = |measured − true|true × 100%
F2: Identify two specific sources of error. For each, state whether it makes g too high or too low and suggest a realistic improvement. Consider simulated sensor variation, reading/rounding, your scale and your best-fit line. Avoid an unsupported “human error” explanation.
Before reflection · Exit Ticket 2
Open the Exit Ticket 2 tab, answer three questions, then return here for reflection.
Reflection 2 min
Write your reflection in your printed lab report.
- Which inquiry skill did you use—questioning, planning, testing or using evidence—and how?
- What are you still unsure about, or what question do you now have?
Return to the WILF card. Tick S for outcomes 3 and 4 if confident; your teacher completes T.
Exit Ticket 1
Three multiple-choice questions. Check each once and read the feedback. Record your score in the printed report.
On your printed report: write one question you got wrong and the correct method, plus one thing you will check more carefully next time.
Exit Ticket 2
Three multiple-choice questions on graphing and data analysis.
Exit Ticket 2 · Check your understanding 3 min
Complete these three multiple-choice questions after Part F and before reflection. Check each answer once, read the feedback, and record your score out of 3 in your printed report beside Session 2 reflection.
On your printed report: note one correction or key idea from this exit ticket before writing your reflection.
Modified Investigation
Acceleration on a Ramp · Small steps for both sessions
My investigation
My question: What happens to acceleration when the ramp angle gets bigger?
Use these guided steps instead of the longer questions in the main sessions. Write answers in your printed modified report, or enter them here and print when finished. The website does not calculate answers for you.
Your entries save on this browser. Print a blank copy now or a completed copy later. A teacher or partner can read the steps with you.
Words to help me
- Angle θ
- How steep the ramp is. Unit: degrees (°).
- Final speed vf
- The speed shown by the photogate. Unit: m/s.
- Acceleration a
- How quickly speed changes. Unit: m/s².
- sin θ
- A number for the angle. Use the values in your table. It has no unit.
- Slope
- How steep a graph line is: rise divided by run.
- Best-fit line
- One straight line close to your points. Do not join the dots.
Collect and calculate
Part A · 25 min Part B · 10 min Exit Ticket 1 · 5 min
Step 1 · Make a prediction DOK 1
We change the angle. We measure final speed and calculate acceleration. We keep the same distance and release from rest.
Step 2 · Collect three measurements DOK 1
Use Δx = 0.50 m, vᵢ = 0 and μₖ = 0 for every run. Use the same cart and ramp.
After each run, return to the Modified Lab Report tab.
| θ (°) | sin θ | Δx (m) | vᵢ (m/s) | vf (m/s) | vf² (m²/s²) | a (m/s²) |
|---|---|---|---|---|---|---|
| 10 | 0.17 | 0.50 | 0 | |||
| 20 | 0.34 | 0.50 | 0 | |||
| 30 | 0.50 | 0.50 | 0 |
The sine values are rounded supports from your Bronze report. Fill the blank columns yourself. Nothing is calculated automatically.
On paper: sketch the ramp. Label the angle, release point, Δx and photogate.
Step 3 · Calculate acceleration DOK 1
The equation is a = vf² − vᵢ²2Δx.
For this method only: vᵢ = 0 and Δx = 0.50 m, so 2Δx = 1.00 m. Square the final speed, then divide by 1.00 m. The numerical value of a equals the numerical value of vf², with different units.
Practice example—not your measurement: if vf = 1.40 m/s, then 1.40 × 1.40 = 1.96 m²/s², so a = 1.96 m/s².
A1 · My working at 20°
Repeat the same steps for 10° and 30°. Complete your table.
A3 · Compare two results DOK 2
Step 4 · Explain Part B · 10 min · DOK 1 & 2
B1 · Use your table to complete the sentence.
Step 5 · Exit Ticket 1 Part C · 5 min
Answer these three supported questions here. Check each answer once and read the feedback. This ticket has its own score and does not change the main Exit Ticket 1.
Graph and compare
Graph 10 min · Analyse 10 min · Evaluate 10 min · Exit Ticket 2 5 min · Reflection 5 min
Step 6 · Draw my graph Part D · 10 min · DOK 1 & 2
- Copy your three acceleration values from your table.
- Use sin θ on the horizontal axis: 0.17, 0.34 and 0.50.
- Use your acceleration values on the vertical axis.
- The axes are numbered for you. Each large square is 0.10 on the horizontal axis and 1 m/s² on the vertical axis. Use the part of the graph needed for your three points.
- Read the axis numbers. Label both axes and add a title.
- Place your three points yourself. Draw one straight best-fit line near them. Do not join the dots.
The website provides axis numbers. You place every data point yourself. Return to this tab after graphing. Download and attach your graph, or copy it onto your printed report.
Step 7 · Read my graph Part E · 10 min · DOK 1 & 2
E2 · Find slope: choose two points far apart on your line. They do not have to be measured points.
Slope = y₂ − y₁x₂ − x₁
E4: sin 90° = 1. Multiply your slope by 1.
This represents acceleration due to gravity. If your line is not close to the origin, ask your teacher before using the simplified equation.
Step 8 · Compare and improve Part F · 10 min · DOK 2
F1: The accepted value of g is 9.8 m/s². Compare it with your slope. You do not need to calculate percentage error for this modified report.
F2 · Choose one error: reading or rounding final speed; reading the angle; plotting a point. For a real ramp, you could also consider wheel friction or pushing the cart.
Step 9 · Exit Ticket 2 Part G · 5 min
Answer these three supported questions here before reflection. This ticket has its own score and does not change the main Exit Ticket 2.
Step 10 · Reflect 5 min · DOK 1 & 2
Your teacher completes T and gives feedback.
Five questions to extend your investigation
Original AP-style practice · No forces knowledge required
Use constant-acceleration relationships, motion graphs and comparisons. Select one answer, then press that question’s Submit answer button to see feedback. Submit each question separately. A submitted answer is final; the other questions remain available.
These are original practice questions, not official College Board exam items. They use separate example data; your lab calculations remain yours to complete.
0 of 5 questions submitted.