Quiz: Potential Energy Calculator
Practise U = m g h with random problems, instant feedback and a worked solution for every question.
🏔️ What is the Potential Energy Quiz?
The Potential Energy Quiz is a practice tool that generates random gravitational potential energy problems, checks your answer instantly and shows a complete worked solution. Gravitational potential energy is the energy an object stores because of its height in a gravitational field. Lift a book onto a shelf and you do work against gravity; that work is stored as potential energy and can be released as motion if the book falls.
The quiz has three levels. Easy gives a mass and a height on Earth and asks for U = m g h, which builds the habit of using consistent units. Medium rearranges the formula, asking for the height or the mass when the energy is known, or asking for the energy on the Moon or Mars where g is different. Hard covers the change in potential energy between two heights (with a sign), the speed of an object dropped from rest by turning potential energy into kinetic energy, and the energy gained by pulling a mass up a ramp.
Students use a quiz like this to prepare for exams and to rehearse the steps that cost marks: choosing the reference level, keeping units consistent and getting the sign right. Teachers can share a level and seed so a class works on the same problem, and tutors can reuse a seed to revisit a question a student missed. The same ideas appear in engineering when sizing a lift, a pumped storage reservoir or a crane load, and in sport when comparing a jump or a dive.
Common misconceptions are worth knowing. Potential energy belongs to the system of object and planet, and its zero is a choice, so only differences are physically meaningful. A ramp does not change the energy gained, because only the vertical rise matters. And the speed of a dropped object does not depend on its mass when air resistance is ignored. Every answer here comes with the arithmetic laid out so these points become concrete.
To compute potential energy for your own numbers, with unit conversions and orbital cases, use the Potential Energy Calculator. This page is for practising the skill yourself, with a score and streak to track progress during a session.
📐 Formulas Used
📖 How to Use This Quiz
Steps to practise potential energy problems
💡 Example Problems
Each example opens the quiz on a specific level and seed with the correct answer filled in, so you see the full worked solution.
Example 1 — Mass on a shelf (Easy, seed 3)
A 30 kg object sits 3 m above the ground (g = 9.8 m/s²). Find its potential energy relative to the ground.
Example 2 — Height on the Moon (Medium, seed 1)
A 17 kg object on the Moon (g = 1.62 m/s²) holds 1101.6 J of potential energy. Find its height.
Example 3 — Speed of a dropped object (Hard, seed 1)
An object is dropped from rest from 33 m on Earth (g = 9.8 m/s²), ignoring air resistance. Find its landing speed.
Example 4 — Moving down (Hard, seed 7)
A 25 kg object moves from 28 m to 21 m on Earth (g = 9.8 m/s²). Find the change in potential energy.
Example 5 — Pulling a mass up a ramp (Hard, seed 2)
A 16 kg mass is moved 5 m along a ramp inclined at 45° (g = 9.8 m/s²). Find the gain in potential energy.
❓ Frequently Asked Questions
🔗 Related Calculators
What is the formula for gravitational potential energy?
Near a planet surface it is U = m g h, mass times gravitational acceleration times height above a chosen reference level. A 30 kg object 3 m above the ground with g = 9.8 m/s squared has U = 30 x 9.8 x 3 = 882 J.
How do I find height from potential energy?
Rearrange U = m g h to h = U / (m g). A 17 kg object holding 1101.6 J on the Moon, where g = 1.62 m/s squared, sits 1101.6 / (17 x 1.62) = 40 m above the reference level.
How do I find mass from potential energy?
Rearrange to m = U / (g h). Divide the energy by g times the height. With 2842 J at 29 m on Earth, m = 2842 / (9.8 x 29) = 10 kg.
Can potential energy be negative?
Yes. Potential energy depends on the zero you choose. An object below the reference level has a negative m g h, and a change in potential energy is negative whenever the object moves down.
How do I find the speed of an object dropped from a height?
If all potential energy becomes kinetic energy, m g h = one half m v squared, so v = sqrt(2 g h). From 33 m on Earth the speed is sqrt(2 x 9.8 x 33) = 25.43 m/s, and the mass does not matter.
How do I use an inclined plane in a potential energy problem?
Convert the slope length to a vertical height with h = L sin(theta), then use U = m g h. Only the vertical rise counts. A 16 kg mass moved up 5 m of a 45 degree ramp rises 3.5355 m and gains 554.37 J.
What tolerance does the quiz accept?
An answer is correct if it is within 1 percent of the exact answer or within 0.01, whichever is larger. This lets you round to two decimals without penalty.
What does the seed do?
The seed is a whole number fed to a pseudo-random generator. The same level and seed always create the identical question, so you can repeat a problem or share it with a classmate. New question picks a fresh random seed.
Does revealing the solution count against my score?
Pressing Show solution marks the question as revealed, so it is not added to your score. Each question is scored only once, on the first check, so rechecking does not inflate your streak.
Which value of g does the quiz use?
Earth problems use g = 9.8 m/s squared, the Moon uses 1.62 and Mars 3.71. The value is printed in every question. If your course uses 9.81 or 9.80665, answers differ by under 0.1 percent, which is inside the tolerance.
Is my score saved?
No. The score and streak are kept only in memory for the current page visit. Reloading resets them, and nothing is stored in your browser or sent anywhere.