A particle is acted upon by three constant forces while it undergoes a displacement

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A particle is acted upon by three constant forces while it undergoes a displacement s=4i+j+3k m\mathbf{s} = 4\mathbf{i} + \mathbf{j} + 3\mathbf{k}\,\text{m}. The forces are F1=10i−5j N\mathbf{F}_1 = 10\mathbf{i} - 5\mathbf{j}\,\text{N}, F2=−6i+3j+2k N\mathbf{F}_2 = -6\mathbf{i} + 3\mathbf{j} + 2\mathbf{k}\,\text{N} and F3=4i+2j−8k N\mathbf{F}_3 = 4\mathbf{i} + 2\mathbf{j} - 8\mathbf{k}\,\text{N}. The particle has mass 1 kg1\,\text{kg} and is initially at rest. (i) Compute the work done by each force during the displacement. (ii) Identify which force does the greatest positive work and which force does the greatest negative work. (iii) Calculate the net work done on the particle. (iv) Determine the speed of the particle after completing the displacement.

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