A box of mass m is pulled with a constant acceleration a along a horizontal frictionless floor by a wire that makes an angle of 15° above th

Question

A box of mass m is pulled with a constant acceleration a along a horizontal frictionless floor by a wire that makes an angle of 15° above the horizontal. If T is the tension in this wire, then _____________.

A) T = ma.
B) T > ma.
C) T < ma.

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Bình An 4 years 2021-08-27T10:40:36+00:00 1 Answers 22 views 0

Answers ( )

  1. Dau
    0
    2021-08-27T10:41:43+00:00
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    Answer:

    B) T > ma.

    Explanation:

    To solve this problem, we have to analyze the forces acting in the horizontal direction.

    In the horizontal direction, we have:

    – The horizontal component of the tension in the wire, Tcos \theta, where T is the magnitude of the tension and \theta the angle that the wire makes with the horizontal

    Since this is the only force acting on the box in the horizontal direction, this is also the net force, so it is equal to the product of mass and acceleration (Newton’s second law of motion):

    Tcos \theta = ma

    where

    m is the mass of the box

    a is the acceleration

    We can rewrite the equation as

    T=\frac{ma}{cos \theta}

    The angle in this problem is \theta=15^{\circ}, so

    T=\frac{ma}{cos 15^{\circ}}=\frac{ma}{0.966}=1.035 ma

    Therefore, the correct option is

    B) T > ma.

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