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23 October, 21:02

Give two mathematical examples of Newton's third law and how you get the solution

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  1. 23 October, 22:57
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    1) Any particle moving in a horizontal plane slowed by friction, deceleration = 32 μ

    2) The particle moving by acceleration = P/m - 32μ OR The external force = ma + 32μm

    Explanation:

    * Lets revise Newton's Third Law:

    - For every action there is a reaction, equal in magnitude and opposite

    in direction.

    - Examples:

    # 1) A particle moving freely against friction in a horizontal plane

    - When no external forces acts on the particle, then its equation of

    motion is;

    ∵ ∑ forces in direction of motion = mass * acceleration

    ∵ No external force

    ∵ The friction force (F) = μR, where μ is coefficient of the frictional force

    and R is the normal reaction of the weight of the particle on the

    surface

    ∵ The frictional force is in opposite direction of the motion

    ∴ ∑ forces in the direction of motion = 0 - F

    ∴ 0 - F = mass * acceleration

    - Substitute F by μR

    ∴ - μR = mass * acceleration

    ∵ R = mg where m is the mass of the particle and g is the acceleration

    of gravity

    ∴ - μ (mg) = ma ⇒ a is the acceleration of motion

    - By divide both sides by m

    ∴ - μ (g) = a

    ∵ The acceleration of gravity ≅ 32 feet/sec²

    ∴ a = - 32 μ

    * Any particle moving in a horizontal plane slowed by friction,

    deceleration = 32 μ

    # 2) A particle moving under the action of an external force P in a

    horizontal plane.

    - When an external force P acts on the particle, then its equation

    of motion is;

    ∵ ∑ forces in direction of motion = mass * acceleration

    ∵ The external force = P

    ∵ The friction force (F) = μR, where μ is coefficient of the frictional force

    and R is the normal reaction of the weight of the particle on the

    surface

    ∵ The frictional force is in opposite direction of the motion

    ∴ ∑ forces in the direction of motion = P - F

    ∴ P - F = mass * acceleration

    - Substitute F by μR

    ∴ P - μR = mass * acceleration

    ∵ R = mg where m is the mass of the particle and g is the acceleration

    of gravity

    ∴ P - μ (mg) = ma ⇒ a is the acceleration of motion

    ∵ The acceleration of gravity ≅ 32 feet/sec²

    ∴ P - 32μm = ma ⇒ (1)

    - divide both side by m

    ∴ a = (P - 32μm) / m ⇒ divide the 2 terms in the bracket by m

    ∴ a = P/m - 32μ

    * The particle moving by acceleration = P/m - 32μ

    - If you want to fin the external force P use equation (1)

    ∵ P - 32μm = ma ⇒ add 32μm to both sides

    ∴ P = ma + 32μm

    * The external force = ma + 32μm
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