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 degrees above the horizontal. The tension in this wire is greater than ma.Group of answer choicesFalseTrue
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 degrees above the horizontal. The tension in this wire is greater than ma.Group of answer choicesFalseTrue
Solution
True. The tension in the wire is greater than ma.
Here's why:
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The tension in the wire can be divided into two components: one horizontal (Tcosθ) and one vertical (Tsinθ).
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The vertical component of the tension (Tsinθ) must balance the weight of the box (mg), so Tsinθ = mg.
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The horizontal component of the tension (Tcosθ) is what's responsible for pulling the box along the floor, so Tcosθ = ma.
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If you combine these two equations, you get T = mg/sinθ = ma/cosθ.
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Since θ is less than 90 degrees, sinθ is less than cosθ, so mg/sinθ is greater than ma/cosθ.
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Therefore, the tension in the wire (T) is greater than ma.
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