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30 April, 21:11

If the only forces acting on a 2.0kg mass are F1 = (3i-8j) N and F2 = (5i+3j) N, what is the magnitude of the acceleration of the particle?

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  1. 30 April, 21:27
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    Answer: 4.7m/s²

    Explanation:

    According to newton's first law,

    Force = mass * acceleration

    Since we are given more the one force, we will take the resultant of the two vectors.

    Mass = 2.0kg

    F1+F2 = (3i-8j) + (5i+3j)

    Adding component wise, we have;

    F1+F2 = 3i+5i-8j+3j

    F1+F2 = 8i-5j

    Resultant of the sum of the forces will be;

    R² = (8i) ² + (-5j) ²

    Since i. i = j. j = 1

    R² = 8²+5²

    R² = 64+25

    R² = 89

    R = √89

    R = 9.4N

    Our resultant force = 9.4N

    Substituting in the formula

    F = ma

    9.4 = 2a

    a = 9.4/2

    a = 4.7m/s²

    Therefore, magnitude of the acceleration of the particle is 4.7m/s²
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