An object on a frictionless surface is being pulled by two strings with force and direction as given in the diagram.
(a) Represent each force as a vector in $R^{2}$ .
(b) Represent the net force being applied to the object as a vector in $R^{2}$ .

Question

An object on a frictionless surface is being pulled by two strings with force and direction as given in the diagram.
(a) Represent each force as a vector in [latex]R^{2}[/latex].
(b) Represent the net force being applied to the object as a vector in [latex]R^{2}[/latex].

Accepted Answer

(a) The force [latex]F_{1}[/latex] has 150N of horizontal force and 0N of vertical force.
Thus, we can represent this with the vector

[latex]\vec{F_{1}} =\left[\begin{matrix} 150 \ 0 \end{matrix} ight] [/latex]

The force [latex]F_{2}[/latex] has horizontal component [latex]100\cos \frac{\pi}{3} =50N[/latex] and vertical component [latex]100\sin \frac{\pi}{3} =50\sqrt{3} N[/latex] Therefore, we can represent this with the vector

[latex]\vec{F_{2}} =\left[\begin{matrix} 50 \ 50\sqrt{3} \end{matrix} ight] [/latex]

(b) We know from physics that to get the net force we add the horizontal components of the forces together and we add the vertical components of the forces together. Thus, the net horizontal component is 150N + 50N = 200N. The net vertical force is 0N + 50√3N = 50√3N. We can represent this as the vector

[latex]\vec{F} =\left[\begin{matrix}200 \ 50\sqrt{3} \end{matrix} ight] [/latex]

Question 1.1.1: An object on a frictionless surface is being pulled by two s...

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