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PhysicsClassical Physics

Newton's First Law: Find the Third Force at Constant Velocity

Use constant velocity to set the net force to zero and find the missing force from two given vectors.

Question

A particle is subject to three forces and has the constant velocity v=(3i^−2j^) m/s\mathbf{v}=(3\hat{\mathbf{i}}-2\hat{\mathbf{j}})\,\mathrm{m/s}. The known forces are F1=(3i^+5j^) N\mathbf{F}_1=(3\hat{\mathbf{i}}+5\hat{\mathbf{j}})\,\mathrm{N} and F2=(4i^−7j^) N\mathbf{F}_2=(4\hat{\mathbf{i}}-7\hat{\mathbf{j}})\,\mathrm{N}. Determine the third force.

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Evidence boundary

This answers Chapter 6 Problem 27 using the exact velocity and force components in the cited University Physics version. It assumes the usual inertial-frame particle model and that the stated three forces comprise the full net force; no measured data or mass is inferred.