6 (a) The magnitude and direction of a force can be represented by a vector - Edexcel - GCSE Physics Combined Science - Question 6 - 2020 - Paper 1

To find the resultant force exerted on the ship from the two boats, begin by representing each tension vector on a diagram.

1. Draw two perpendicular vectors: Each tension vector (20 kN) forms a right angle. Label them T1 and T2.
2. Apply the Pythagorean theorem: Since the vectors are at right angles, the resultant force (R) can be calculated using: $R = \\sqrt{T_1^2 + T_2^2} = \\sqrt{(20 \\text{ kN})^2 + (20 \\text{ kN})^2} = \\sqrt{400 + 400} = \\sqrt{800} \\approx 28.28 \\text{ kN}$

The magnitude of the resultant force that the boats exert on the ship is approximately 28.3 kN.

To maintain a constant horizontal velocity, all the forces acting on the wooden block must be balanced:

1. Horizontal Forces: The tension in the string pulls the block forward, while friction between the table and the block opposes this motion. The force due to friction is equal to the tension, allowing motion without acceleration.

   • Tension in the string acts in the direction of motion.
   • Friction opposes motion and is equal to the tension, thus: $F_{friction} = F_{tension}$

2. Vertical Forces: The normal reaction force from the table balances the gravitational force acting downward on the block (due to its weight).

   • The weight of the block acts downwards, while the normal force acts upwards.
   • These forces are also equal and opposite: $F_{normal} = F_{weight}$

Since the forces are balanced, the net force is zero, and as a result, the block moves across the table at a constant horizontal velocity.