A block of mass $$$5 \mathrm{~kg}$$$ is being pulled along a rough horizontal floor by a force of magnitude $$$X \mathrm{~N}$$$ acting at $$$30^{\circ}$$$ above the horizontal (see diagram). The block starts from rest and travels $$$2 \mathrm{~m}$$$ in the first $$$5 \mathrm{~s}$$$ of its motion. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_m21_qp_42 Year：2021 Question No：5(b)

Answer:

$R=5 g-X \sin 30$
$X \cos 30-F=5 a$
$X \cos 30-0.4(5 g-X \sin 30)=5 \times 0.16$
$X=19.5(3 \mathrm{sf})$

Knowledge points:

4.1.1 identify the forces acting in a given situation； e.g. by drawing a force diagram.

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.）

4.1.4 understand that a contact force between two surfaces can be represented by two components, the normal component and the frictional component

4.1.6 understand the concepts of limiting friction and limiting equilibrium, recall the definition of coefficient of friction, and use the relationship F = nR or F G nR, as appropriate

4.4.1 apply Newton’s laws of motion to the linear motion of a particle of constant mass moving under the action of constant forces, which may include friction, tension in an inextensible string and thrust in a connecting rod If any other forces resisting motion are to be considered (e.g. air resistance) this will be indicated in the question.

Answer:

Knowledge points:

Solution:

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