A railway engine of mass $$$75000 \mathrm{~kg}$$$ is moving up a straight hill inclined at an angle $$$\alpha$$$ to the horizontal, where $$$\sin \alpha=0.01$$$. The engine is travelling at a constant speed of $$$30 \mathrm{~m} \mathrm{~s}^{-1}$$$. The engine is working at $$$960 \mathrm{~kW}$$$. There is a constant force resisting the motion of the engine. Find the resistance force. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w21_qp_42 Year：2021 Question No：5(a)

Answer:

Driving force $=D F=\frac{960000}{30}$
$D F-75000 g \times \sin \alpha-R=0$
Resistance force $=R=24500 \mathrm{~N}$

Knowledge points:

4.1.2 understand the vector nature of force, and find and use components and resultants； Calculations are always required, not approximate solutions by scale drawing.

4.1.3 use the principle that, when a particle is in equilibrium, the vector sum of the forces acting is zero, or equivalently, that the sum of the components in any direction is zero （Solutions by resolving are usually expected, but equivalent methods (e.g. triangle of forces, Lami’s Theorem, where suitable) are also acceptable; these other methods are not required knowledge, and will not be referred to in questions.）

4.5.4 use the definition of power as the rate at which a force does work, and use the relationship between power, force and velocity for a force acting in the direction of motion Including calculation of (average) power;P = Fv

Answer:

Knowledge points:

Solution:

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