A constant force acts on a block that undergoes a displacement ; at one instant…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Tensors and differential geometry · Tensors and differential geometry

Invariance, Ch Index notation and Cartesian tensors

Problem

A constant force F=(3,−2,5) N\mathbf{F} = (3, -2, 5)\,\mathrm{N} acts on a block that undergoes a displacement x=(1,4,−2) m\mathbf{x} = (1, 4, -2)\,\mathrm{m}; at one instant during the motion its velocity is v=(2,0,−1) m s−1\mathbf{v} = (2, 0, -1)\,\mathrm{m\,s^{-1}}. ((a)) Write the work done, W=F⋅xW = \mathbf{F}\cdot\mathbf{x}, and the instantaneous power, P=F⋅vP = \mathbf{F}\cdot\mathbf{v}, using the summation convention, and say how many free indices each expression has. ((b)) Evaluate WW and PP numerically.

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