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.

In Standard, the last three questions ask for acceleration. Find the push minus friction, then use a = F ÷ m to get the acceleration 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. Challenge starts with right angles, then asks for acceleration. Practice mode turns the timer off.

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.

• 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.