A-LevelMathematicsMechanics9709/41 · Oct/Nov 2018 · Q59 Marks
Coplanar forces, of magnitudes 15 N, 25 N and 30 N, act at a point B on the line ABC in the directions shown in the diagram. [Figure 5.1]
- (i)Find the magnitude and direction of the resultant force.[6]
- (ii)The force of magnitude 15 N is now replaced by a force of magnitude F N acting in the same direction. The new resultant force has zero component in the direction BC. Find the value of F, and find also the magnitude and direction of the new resultant force.[3]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [M1] For resolving forces horizontally or vertically o.e.
- [A1] 25 cos 30 - 15 cos 40 (= 10.1599...)
- [A1] 25 sin 30 + 15 sin 40 – 30 (= -7.8581...)
- [M1] For using a method for either magnitude or direction
- [A1] Magnitude = 12.844...
- [A1] Angle 37.7° below the horizontal in the direction BA
- [M1] For equating forces in the direction BC to zero
- [A1] F = 28.2628...
- [B1] New resultant force = 28.26...sin 40 + 25 sin 30 - 30 = 0.667 N upwards
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