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Q.

With two hands, you hold a cone motionless upside down, as shown in figure. The mass of the cone is (m = 1 kg), and the coefficient of static friction between you fingers and the cone is (μ=0.5). If the minimum normal force you must apply with each hand in order to hold up the cone is found to be 13n N. find the value of 'n' . Consider only translational equilibrium.

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answer is 5.

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Detailed Solution

For equilibrium in vertical direction Here θ is the base angle of the cone .2fsin⁡θ−2Ncos⁡θ−mg=0       2μNsin⁡θ−2Ncos⁡θ=mg …………1tanπ2−θ=512cot⁡θ=512,sin⁡θ=1213 & cos⁡θ=5122(0.5)1213N−2N⋅513=(1)(10)N = 65 N Hence n=5
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