5.5 Resolving forces and vector diagrams
8 exam questions worth 24 marks. Write your answer, open the mark scheme, then give yourself the marks you earned. Your answers are saved on this device.
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Two forces of 9 N and 12 N act on an object at right angles to each other. Calculate the size of the resultant force.
Mark scheme
resultant² = 9² + 12² (1); √225 (1); 15 N (1)
Model answer
Resultant = √(9² + 12²) = √225 = 15 N.
A scale drawing is used to find the resultant of two forces. State the scale you would use for a 6 N force and a 8 N force on A4 paper, and describe how to draw the diagram.
Mark scheme
a suitable scale e.g. 1 cm for 1 N (1); draw the first force to scale in the correct direction (1); draw the second force from the head of the first (head-to-tail) (1); draw the resultant from the start to the end and measure its length and angle (1)
Model answer
Use a scale such as 1 cm for 1 N. Draw the first force to scale, then draw the second from the head of the first. The resultant is the line from the start to the end, and its length gives the size of the force.
A force of 40 N acts at 60° above the horizontal. Calculate the horizontal component of the force.
Mark scheme
F cos θ = 40 × cos 60° (1); 20 N (1)
Model answer
Horizontal component = 40 × cos 60° = 20 N.
A rope pulls a box with a force of 200 N at 30° above the horizontal. Calculate (a) the horizontal component and (b) the vertical component.
Mark scheme
(a) 200 × cos 30° (1); 173 N (1); (b) 200 × sin 30° (1); 100 N (1)
Model answer
(a) Horizontal = 200 × cos 30° = 173 N. (b) Vertical = 200 × sin 30° = 100 N.
Explain what is meant by resolving a force.
Mark scheme
splitting a force into two components (1); at right angles to each other (1)
Model answer
Resolving a force means splitting it into two components that act at right angles to each other, with the same effect as the original force.
A 4 N force and a 3 N force act on an object at right angles to each other. A third force is needed to keep the object in equilibrium. State the size and direction of this third force.
Mark scheme
the resultant of the 4 N and 3 N forces is 5 N (1); the third force is 5 N (1); in the opposite direction to the resultant (1)
Model answer
The resultant of the two forces is √(4² + 3²) = 5 N, so the third force is 5 N, acting in the opposite direction to the resultant.
The vector triangle for three forces acting on an object is closed. Explain what this tells you about the object.
Mark scheme
the resultant force is zero / the forces are balanced (1); the object is in equilibrium: at rest or moving with constant velocity (1)
Model answer
A closed triangle means the resultant force is zero, so the object is in equilibrium and is either at rest or moving at a constant velocity.
A force of 10 N acts to the east and a force of 10 N acts to the north. Calculate the size of the resultant force, and its direction relative to east.
Mark scheme
√(10² + 10²) (1); 14 N (1); tan θ = 10 ÷ 10 (1); 45° north of east (1)
Model answer
Resultant = √(10² + 10²) = 14 N. tan θ = 10/10 = 1, so θ = 45°. The resultant is 14 N at 45° north of east.
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