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Answers · Resultant force

Resultant force — return questions key

Check meaning, not exact wording. These are teaching points, not official Cambridge marks.

1. FR1 · Return

Model answer. (a) The resultant force is the single force that would have the same effect as all the forces on the object together. (b) The forces to the left add up to 30 N + 15 N = 45 N, which balances the 45 N to the right, so the resultant force is zero. (c) The cupboard stays at rest, so the resultant force on it is zero. The push of 120 N to the right must be balanced by another horizontal force of 120 N to the left: friction from the floor. (d) A resultant force can change the speed of an object, its direction of motion, or both. (e) (i) A force towards the west acts against her motion, so she slows down; if the wind keeps pushing, she stops and then moves west, faster and faster. (ii) A force towards the north is at right angles to her motion, so her path curves towards the north.

A full answer includes

  • (a) The single force that has the same effect as all the forces on the object together.
  • (b) Method: 30 N + 15 N = 45 N to the left.
  • (b) Answer: 45 N to the left balances 45 N to the right, so the resultant is zero.
  • (b) I did not add all three forces to get 90 N.
  • (c) The resultant force is zero, because the cupboard stays at rest.
  • (c) The other force is 120 N, to the left.
  • (d) By changing its speed.
  • (d) By changing its direction of motion.
  • (e)(i) She slows down, stops, then moves back west, faster and faster.
  • (e)(ii) Her path curves towards the north.
  • (e) I did not write that she stops at once.

Also accept

  • (a) the single force with the same effect as all of them; (b) zero; (c) zero, and 120 N to the left (friction); (d) its speed and its direction; (e) (i) slows, stops, comes back; (ii) curves north.

Watch for

  • “(b) The resultant is 90 N.” — Forces in opposite directions take away: 45 N to the right and 45 N to the left give zero.
  • “(c) There is no other force: the push is just too small to move the cupboard.” — If the push were the only horizontal force, the cupboard would start to move. It stays at rest, so another force, friction from the floor, balances it: 120 N to the left.
  • “(e)(i) The skater stops at once.” — The force changes her velocity gradually: she slows down, stops, and then comes back.

2. FR2 · Return

Model answer. (a) Weight is a force: it has a size and a direction, downwards, towards the centre of the Earth, so it is a vector. Mass has a size only; it does not point anywhere, so it is a scalar. (b) With 1 cm = 0.20 m/s, the 1.6 m/s arrow is 1.6 ÷ 0.20 = 8.0 cm long, and the 0.90 m/s arrow 4.5 cm. The resultant arrow of 9.2 cm stands for 9.2 × 0.20 = 1.84 m/s, about 1.8 m/s. A calculation agrees: √(1.6² + 0.90²) = 1.84 m/s. (c) Resultant force = mass × acceleration, F = ma, with F in newtons, m in kilograms and a in m/s². (d) m = F ÷ a = 0.45 N ÷ 1.5 m/s² = 0.30 kg. The acceleration is towards the north, the direction of the resultant force. (e) A bigger pull with the same mass and radius goes with a bigger speed. A bigger pull with the same mass and speed bends the path more tightly, so the radius decreases.

A full answer includes

  • (a) Weight is a force, so it has a size and a direction: downwards.
  • (a) Mass has a size only, with no direction, so it is a scalar.
  • (b) Method: 1.6 m/s ÷ 0.20 m/s per cm.
  • (b) Answer: the arrow is 8.0 cm long.
  • (b) Method: 9.2 cm × 0.20 m/s per cm.
  • (b) Answer: the resultant velocity is 1.84 m/s, about 1.8 m/s.
  • (b) I did not add the velocities to get 2.5 m/s.
  • (c) F = ma.
  • (c) F in newtons (N), m in kilograms (kg), a in metres per second squared (m/s²).
  • (d) Method: m = F ÷ a = 0.45 N ÷ 1.5 m/s².
  • (d) Answer: m = 0.30 kg.
  • (d) The acceleration is towards the north, the direction of the force.
  • (e)(i) The speed increases.
  • (e)(ii) The radius decreases: the circle gets smaller.

Also accept

  • (a) weight is a force, with a direction; mass has a size only; (b) 8.0 cm, then about 1.8 m/s; (c) F = ma, N, kg, m/s²; (d) 0.30 kg, north; (e) (i) the speed increases; (ii) the radius decreases.

Watch for

  • “(b) The resultant velocity is 2.5 m/s.” — The velocities are at right angles, so they do not simply add. Read the size from the 9.2 cm arrow with the scale.
  • “(b) The arrow for 1.6 m/s is 0.32 cm long.” — You multiplied by the scale. Each centimetre stands for 0.20 m/s, so 1.6 m/s needs many centimetres: divide.
  • “(d) The mass is 0.675 kg.” — You multiplied. m = F ÷ a = 0.45 ÷ 1.5 = 0.30 kg.
  • “(e)(ii) A bigger pull makes the circle bigger.” — The string pulls inwards. A bigger inward pull at the same speed bends the path more tightly, into a smaller circle.