How to play Resultant Force
Resultant Force is a GCSE physics game about the resultant force on an object. Each question shows a free body diagram: a box with force arrows on it, each labelled in newtons. You pick the right answer from four choices.
The first three questions have two forces along one line, pulling in opposite directions. You find the size of the resultant and which way it points. Questions 4 to 7 have two forces at right angles, one to the right and one upwards. This time you find the size of the resultant and its angle above the horizontal.
The last three questions add a mass. A pushing force acts one way and a smaller force acts against it, and you find the acceleration of the box in m/s². Some masses are in grams, so convert them to kilograms first.
Each right answer scores 10 points, with 5 more for answering inside 15 seconds. After every answer the game shows the working, right or wrong. The harder start begins with the forces at right angles. Practice mode turns the timer off.
The science behind resultant forces
A resultant force is the single force that has the same effect as all the forces on an object acting together. If the forces balance, the resultant is zero. The object then stays still, or keeps moving at the same speed in the same direction.
When two forces act along the same line, you add them if they point the same way and subtract if they point opposite ways. A box pulled right with 18 N and left with 5 N has a resultant of 13 N to the right. The resultant always points the same way as the larger force, so the direction is part of the answer.
Forces at right angles need a different method. Draw the two forces nose to tail, then join the start of the first to the end of the second. That line is the resultant, and it is the longest side of a right-angled triangle. With forces of 6 N and 8 N, Pythagoras' theorem gives √(6² + 8²) = √100 = 10 N. The same triangle gives the angle. The exam boards ask for this with scale drawings, and a careful drawing gives the same answer as the calculation.
Newton's second law links the resultant force to acceleration: F = m a. A bigger resultant force gives a bigger acceleration, and a bigger mass gives a smaller one. Rearranged, a = F ÷ m. A 4 kg box with a 60 N push and 20 N of friction has a resultant of 40 N, so it accelerates at 40 ÷ 4 = 10 m/s². The mass has to be in kilograms. If you put 4,000 g into the equation, the answer is 1,000 times too small.
AQA (8463) covers resultant forces in section 4.5.1.4 and Newton's second law in 4.5.6.2.2. On AQA, finding the resultant of two forces at an angle with a vector diagram is Higher tier only. Edexcel (1PH0) covers vector diagrams and free body diagrams in points 9.3 to 9.5 and F = m a at 2.15. OCR Gateway (J249) covers them in P2.2e and P2.2g, with Newton's second law at P2.2i.
Tips for finding the resultant force
- Before you calculate, look at which way each arrow points. Opposite arrows subtract, and arrows in the same direction add.
- For two forces at right angles, the resultant is bigger than either force but smaller than their sum. If you added 6 N and 8 N to get 14 N, go back.
- Check the direction as well as the size. The right number with the wrong direction still counts as wrong.
- Find the resultant force before you use F = m a. The push on its own ignores the friction.
- Change grams to kilograms by dividing by 1,000.
- Acceleration is force divided by mass. A heavier box gets less acceleration from the same force, so m ÷ F cannot be right.
Use Resultant Force in the classroom
Resultant Force suits Years 9 to 11. The first three questions work for any GCSE class, and the right-angle questions suit Years 10 and 11, and on AQA they are Higher tier. Ten questions take about five minutes.
Use it as a starter before a forces lesson. Put a question on the board and ask students to sketch the free body diagram and draw the resultant arrow before anyone chooses. For the right-angle questions, students can check the game's answer with a quick scale drawing on squared paper, which is the method the boards ask for.
The wrong options show real mistakes: adding forces that act in opposite directions, getting the direction backwards, adding forces at right angles and forgetting to convert grams. Pause after a wrong answer and ask the class which mistake it was.
Practice mode removes the 15-second timer. The game runs in the browser with no login. Teachers can find more lesson ideas on the teachers page, and the about page explains how we check the physics in every game.
Similar games
See all our games for more. Equation Rearranger gives more practice with F = m a and other force equations, and Unit Sprint drills conversions such as grams to kilograms. For motion under gravity, our sister site has Projectile Motion.
Questions people ask
Here are the questions students and teachers ask most about resultant forces.
How do you find the resultant of two forces at right angles?
Draw them nose to tail to make a right-angled triangle. The resultant is the longest side, so use Pythagoras' theorem or a scale drawing. Forces of 5 N and 12 N give a resultant of 13 N.
What happens when the resultant force is zero?
The forces are balanced. An object that is still stays still, and a moving object keeps the same speed and direction.
How do you calculate acceleration from a free body diagram?
Find the resultant force first by combining all the forces. Then divide it by the mass in kilograms, using a = F ÷ m. The answer is in m/s².
Is finding the resultant of forces at an angle a Higher tier topic?
On AQA it is. Finding the resultant of two forces at an angle with a vector diagram is Higher tier only, while forces along a straight line are on both tiers. Check your own board's specification for its tiers.