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A block is hung by a string from the inside roof of a van. When the van goes straight ahead at a speed of 29 m/s, the block hangs vertically down. But when the van maintains this same speed around an unbanked curve (radius = 170 m), the block swings toward the outside of the curve. Then the string makes an angle with the vertical. Find .
=___ °

2007-10-13 02:00:47 · 3 answers · asked by Santina E 1 in Science & Mathematics Physics

3 answers

mv²/r is directed along the x axis
mg is directed down the y axis
the components of these forces along the direction of motion of the block are mv²cosθ/r & -mgsinθ and since the system is in equilibrium
0 = ∑F = mv²cosθ/r + (-mgsinθ)
gives
sinθ/cosθ = v²/gr
so
tanθ = v²/gr
θ ≈ 26.8

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2007-10-13 02:22:59 · answer #1 · answered by The Wolf 6 · 1 0

Resolving the tension T in the string,

Its horizontal component provides the centripetal force for the bob which is also in circular motion of radius R.
T sin θ = mv^2 / R. -----------------------------1

Its vertical component,
T cos θ = mg, ---------------------------2.
Since, it balances the weight of the bob.

Dividing 1by 2.
tan θ = v^2 / Rg = 29^2 / 170 x 9.8
θ = 26.78°

2007-10-13 11:28:38 · answer #2 · answered by Pearlsawme 7 · 0 0

What is it about the question you find confusing? I understand it perfectly well. Oh, I get it; you're confused about how to find the *answer*. That's completely different. Never mind :-)

2007-10-13 12:26:45 · answer #3 · answered by Dr. R 7 · 0 0

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