One question runs through today: when an object’s mass or speed changes, what happens to its kinetic energy? You’ll guess first, calculate, then test it on a rolling cart and find the rule the numbers follow.
🎯 Goals
- Calculate kinetic energy in joules from mass and speed using KE = ½mv².
- Test how KE changes when you change an object’s speed, and when you change its mass.
- Discover the doubling rules: ×2 mass gives ×2 KE, ×2 speed gives ×4 KE.
- Use KE and the work-energy theorem to explain why fast objects need so much more room to stop.
🧰 Materials
🚗A free-rolling toy car or lab cart
🪙Loads to add mass (coins or washers) and tape to hold them in place
🛝A smooth board about 1 m long, plus books to prop it up
📏Meter stick or tape measure, plus masking tape for start and finish lines
⏱️Stopwatch or phone (slow-motion video works best)
⚖️A scale that reads in grams
🧮Calculator
📓Physics notebook
Section 1 of 4
Gut Check: Who Carries the Most Energy?
1
Rank the five objects by gut feeling.
Look at the mass and speed of each object in the table below. Without calculating, write them in your notebook from least to most kinetic energy.
KE = ½ × m × v²
Mass m is in kilograms and speed v is in meters per second. Square the speed first, then multiply by the mass, then take half. The answer is in joules (J).
2
Calculate the KE of each object.
Enter your answers below. The tool checks each one and then shows the true ranking so you can compare it with your guess.
KE Builder
Rank first, then calculate. Enter each KE in joules. A correct answer is within 2%.
📓 Physics Notebook
Which result surprised you most? Explain why a slow-moving car can carry far more energy than a fast-moving baseball.
Section 2 of 4
Lab A: Change the Speed
3
Build a ramp with a flat run-out.
Prop one end of the board on books so the cart can roll down onto a flat floor or table. Tape a start line where the cart reaches the flat, and a finish line 1.5 m beyond it. Put a book past the finish line to stop the cart.
4
Find the cart’s mass.
Mass it in grams, then divide by 1000 to get kilograms. Write it at the top of your table.
5
Release the cart from rest at three heights: 5 cm, 10 cm, and 20 cm.
Measure each height straight up from the flat surface to the cart’s release point. Let go without pushing. Start the timer as the cart crosses the start line and stop it at the finish line. Do three runs per height and average them.
⚠️ Hand timing is rough. Slow-motion phone video, stepped frame by frame, is more accurate. Expect some scatter. The pattern in your numbers matters more than any single value.
6
Calculate speed, speed squared, and KE for each height.
On the flat run-out the cart moves at nearly constant speed, so v = 1.5 m ÷ average time. Then find v², then KE = ½mv².
📓 Physics Notebook
Compare your 5 cm and 20 cm rows. The height went up by 4 times. By about how many times did the speed go up? By how many times did KE go up? Which doubling rule does that remind you of?
Section 3 of 4
Lab B: Change the Mass
7
Hold the release height at 10 cm and add mass.
Run the cart with no load, then with one load taped on, then with two loads. Keep the loads in the same spot each time. Measure the total mass after each change, in kilograms.
8
Time three runs for each mass and calculate speed and KE.
Use the same 1.5 m timing zone and the same formulas as Lab A.
📓 Physics Notebook
As you added mass, what happened to the speed? What happened to the KE? Explain why KE changed even though the cart started from the same height. If the heavier runs were a bit slower, what might explain that?
✅ Lab check: both tables complete and at least one row verified with the KE Checker. Clean up your ramp and loads before moving on.
Section 4 of 4
Find the Rules, Then Use Them
9
Complete the Doubling Rules Challenge.
Use KE = ½mv² and your lab results. Work out how KE scales before you type, then check.
Doubling Rules Challenge
KE becomes how many times as big? Enter a number or a fraction like 1/4. Think about which quantity is squared.
10
Connect KE to work: how far does a car need to stop?
Use the work-energy theorem from Activity 4-1-1. Friction does negative work equal to the car’s KE, so the braking distance is d = KE ÷ F.
Brake Check
A 1,000 kg car brakes to a stop with a constant 8,000 N of friction. The brakes must do negative work equal to the car’s KE, so d = KE ÷ F. Find the stopping distance.
Question 1
Use your Lab A data to explain why KE grew faster than speed did. Include your v² column.
Question 2
Use your Lab B data to explain why KE went up with mass even though the speed stayed about the same.
Question 3
A baseball (0.145 kg at 40 m/s) has about the same KE as a bowling ball (6.0 kg at 6.0 m/s). Explain how a small, light object can match a heavy one.
Question 4
A pendulum bob swings down and back up. Where in its swing do you expect the greatest KE, and why? (You’ll test this in Project 4-1-4.)
📤 Turn In
- Your gut ranking from Step 1 and the notebook note on what surprised you
- Completed Lab A table, with the 5 cm vs. 20 cm comparison
- Completed Lab B table, with your explanation of what mass did to speed and KE
- Your results from the Doubling Rules Challenge and Brake Check
- Written answers to the four Conclusion questions