9. (a) The magnitude and direction of a force can be represented by a vector. Figure 22 shows the forces acting on four identical trolleys. The arrows show the magnitude and direction of the forces. Which diagram shows a pair of forces that will produce zero acceleration? (1) (b) Figure 23 shows two small boats pulling a much larger ship. The ship is connected to the boats with ropes. The tension, T, in each of the ropes has a magnitude of 20 kN. The ropes are at right angles to each other. Draw a vector diagram and use it to determine the resultant force that the boats exert on the ship. (4) (c) Figure 24 shows a wooden block connected to a weight by a string. The string goes over a pulley. The surfaces of the table and the wooden block are both rough. The wooden block moves across the table at a constant horizontal velocity. Several vertical and horizontal forces act on the wooden block as it moves. Explain how the forces keep the wooden block moving across the table at a constant horizontal velocity. Your answer should refer to all forces acting on the wooden block.

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9. (a) The magnitude and direction of a force can be represented by a vector - Edexcel - GCSE Physics - Question 9 - 2020 - Paper 1

Question 9

9. (a) The magnitude and direction of a force can be represented by a vector. Figure 22 shows the forces acting on four identical trolleys. The arrows show the magn... show full transcript

Worked Solution & Example Answer:9. (a) The magnitude and direction of a force can be represented by a vector - Edexcel - GCSE Physics - Question 9 - 2020 - Paper 1

Step 1

Determine the resultant force on the ship

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Answer

To find the resultant force exerted by the boats on the ship, we can represent the tension in the ropes as vectors. Given that the tension, T, in each of the ropes is 20 kN and they are at right angles, we can use the Pythagorean theorem to determine the resultant vector.

The formula for the resultant force, R, is given by:

$R = \sqrt{T^2 + T^2} = \sqrt{(20 ext{ kN})^2 + (20 ext{ kN})^2}$

Calculating this gives:

$R = \sqrt{400 + 400} = \sqrt{800} = 20\sqrt{2} ext{ kN} \approx 28.28 ext{ kN}$

Thus, the magnitude of the resultant force on the ship is approximately 28.28 kN.

Step 2

Explain how the forces keep the wooden block moving

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Answer

The wooden block on the table experiences several forces as it moves at a constant horizontal velocity. These forces can be categorized as follows:

Horizontal Forces

Tension in the string: The tension in the string pulls on the wooden block, providing a horizontal force. This is one of the forces acting on the block, aiding its movement across the table.
Friction: There is friction between the table and the wooden block. This frictional force acts in the opposite direction to the tension and opposes motion. The value of the friction depends on the normal force and the coefficient of friction between the two surfaces.
Balance of Forces: The forces are balanced, meaning that the force of tension provided by the string is equal to the opposing friction force. As a result, there is no resultant force, allowing the wooden block to move at a constant velocity.

Vertical Forces

Weight of the Block: The block has a weight acting downwards due to gravity. This weight provides a normal reaction force from the table upwards.
Normal Reaction Force: There is a normal reaction force acting upwards, which balances the weight of the block. These forces are equal and opposite, and do not affect the horizontal motion of the block.

In summary, the balance between tension and friction along with the equilibrium of vertical forces allows the block to maintain a constant horizontal velocity.

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