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A smooth inclined plane (angle 37 deg) is fixed inside a box that accelerates at a = 5i + 10j m/s² (horizontal + vertical) in a vertical plane. A block of mass 1 kg rests on the incline and is connected by a wire (cross-sectional area 0.1 cm², length 1.5 m, Young's modulus Y = 3 * 10¹⁰ N/m²) aligned along the incline. The block is in equilibrium relative to the incline. Find the extension of the wire. (g = 10 m/s², sin 37 deg = 3/5, cos 37 deg = 4/5)
- 8 * 10⁻⁵ m
- 6 * 10⁻⁵ m
- 8 * 10⁻⁶ m
- None of these
Correct answer: 8 * 10⁻⁵ m
Solution
In the box's non-inertial frame, the pseudo-force is -m*a = -(5i+10j) N. Resolving along the incline (up-incline positive): gravity contributes -mg sin37 = -6 N and pseudo-force contributes -(5*cos37 + 10*sin37) = -10 N. The wire tension T = 16 N acts up the incline. Extension = TL/(AY) = 16*1.5/(10⁻⁵ * 3*10¹⁰) = 24/(3*10⁵) = 8*10⁻⁵ m.
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