The problems are on the resultant force worksheet. Try them on your own first, then compare with the answers below.
Quick answer: A resultant force is the single force that has the same effect as all the forces acting on an object. These worked answers correct the 20 problems of the Physics 9-10 worksheet on resultant force, from name the force to spot the errors: each solution shows the formula, the substitution and the final answer with its unit.
Each answer states the rule used, the substitution and the final value in bold with its unit and direction. Remember that a resultant force always needs a direction as well as a size.
Level: Physics grades 9-10 (GCSE · IGCSE · O Level · Class 9-10) · Curriculum: GCSE P5
Problem 1 Name the force
1. weight (gravity).
2. friction.
3. drag (air resistance).
4. upthrust.
5. tension.
Problem 2 Weight of a bag
1. W = m g.
2. W = 4.5 × 9.8 = 44.1, so 44 N.
3. Downwards, towards the centre of the Earth.
Problem 3 Forces in the same direction
1. 200 + 150 = 350 N.
2. In the direction of the push.
Problem 4 Forces in opposite directions
1. 90 − 60 = 30 N.
2. To the right, the direction of the larger force.
Problem 5 Balanced or unbalanced
1. balanced (resultant 0 N).
2. unbalanced (5 N right).
3. unbalanced (16 N right).
4. balanced (resultant 0 N).
Problem 6 Reading a diagram
1. A is the weight, B is the normal reaction, C is the pull (tension) and D is friction.
2. A and B are equal because there is no vertical movement.
3. To the right, in the direction of C.
Problem 7 Car on the road
1. 3000 − 1800 = 1200 N forward.
2. The car speeds up.
3. The forces balance, so the car moves at a constant speed in a straight line.
Problem 8 Steady cycling
1. The resultant force is 0 N.
2. The resistive forces total 85 N backwards.
3. Constant velocity means no change of motion, so the forward and backward forces must balance.
Problem 9 Three forces on a line
1. 40 + 25 = 65 N.
2. 90 − 65 = 25 N west.
Problem 10 Standing on a scale
1. W = 55 × 9.8 = 539 N.
2. 539 N upwards.
3. He is at rest, so the resultant is zero and the reaction equals the weight.
Problem 11 Pulling a crate
1. Constant speed means balanced forces, so friction is 150 N backwards.
2. 210 − 150 = 60 N forward.
3. The crate speeds up in the direction of the pull.
Problem 12 Two forces at right angles
1. R² = 6.0² + 8.0² = 36 + 64 = 100, so R = 10 N.
2. tan θ = 8.0 ÷ 6.0 = 1.33, so θ = 53°.
Problem 13 Scale drawing
1. 15 ÷ 5 = 3.0 cm and 20 ÷ 5 = 4.0 cm.
2. √(3.0² + 4.0²) = √25 = 5.0 cm.
3. 5.0 × 5 = 25 N.
Problem 14 Hanging lamp
1. W = 3.5 × 9.8 = 34.3 N (about 34 N).
2. The lamp is in equilibrium, so the tension equals the weight: 34.3 N upwards.
Problem 15 Rising balloon
1. Constant speed, so the resultant is 0 N.
2. Upward force = downward forces: 6500 = W + 300, so W = 6200 N.
Problem 16 Towing a boat
1. R² = 120² + 160² = 14 400 + 25 600 = 40 000, so R = 200 N.
2. tan θ = 160 ÷ 120 = 1.333, so θ = 53° north of east.
3. The boat accelerates in the direction of the resultant, 53° north of east.
Problem 17 A ring in equilibrium
1. R = √(30² + 40²) = 50 N at 53° north of east.
2. The third force is 50 N at 53° south of west, the opposite direction.
3. The ring is in equilibrium, so the total resultant is zero and the third force must cancel the first two.
Problem 18 Push a handcart
1. 260 − 100 = 160 N forward.
2. a = F ÷ m = 160 ÷ 80 = 2.0 m/s².
3. W = 80 × 9.8 = 784 N. The cart does not move vertically, so the reaction is 784 N upwards.
Problem 19 Parachute opens
1. W = 75 × 9.8 = 735 N down.
2. Drag exceeds weight: 1500 − 735 = 765 N upwards.
3. The resultant is upward, so she slows down while still falling.
Problem 20 Spot the errors
1. The book is at rest, so the upward reaction must equal the weight: both 8.0 N.
2. There is no horizontal force on a book at rest, and there is no force called “motion”, so the arrow must be removed.
3. Forces still act, but they are balanced, so the resultant is zero.
