A hockey puck of mass rests on a nearly frictionless horizontal ice rink

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

Problem

A hockey puck of mass 0.25 kg0.25\,\text{kg} rests on a nearly frictionless horizontal ice rink. Three forces act on the puck in the plane of the ice: • F⃗1=⟨3.0, −2.0⟩ N\vec F_{1}=\langle 3.0,\,-2.0\rangle\,\text{N} • F⃗2=⟨−1.0, +4.0⟩ N\vec F_{2}=\langle -1.0,\,+4.0\rangle\,\text{N} • An additional force F⃗3\vec F_{3} that can be chosen freely. Unit vectors ı^\hat{\imath} and ȷ^\hat{\jmath} point east and north, respectively. The rink manager wants the puck to accelerate at 10.0 m s−210.0\,\text{m}\,\text{s}^{-2} in a direction exactly 45∘45^{\circ} north of east. (a) Express the desired acceleration vector in component form. (b) Derive an expression for the required net force on the puck in component form. (c) Determine the components, magnitude, and direction of F⃗3\vec F_{3} that will produce the required acceleration. (d) Verify that the magnitude of the actual acceleration produced by your chosen F⃗3\vec F_{3} equals 10.0 m s−210.0\,\text{m}\,\text{s}^{-2} within appropriate numerical precision.

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