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Question:

Consider an elliptically shaped rail PQ in the vertical plane with OP=3m and OQ=4m. A block of mass 1 kg is pulled along the rail from P to Q with a force of 18 N, which is always parallel to line PQ (see the figure given). Assuming no frictional losses, the kinetic energy of the block when it reaches Q is (n×10) Joules. The value of n is (take acceleration due to gravity=10 ms⁻²)

Solution:

Using work energy principle, ΣWD = ΣKE
∴ −mgh + F⋅x = KE
∴ −(1)(10)(4) + 18 × √4² + 3² = KE
∴ KE = 50
∴ n = 5