An object that weighs 10kg is being pulled by two strings with force and direction as given in the diagram. Newton’s second law of motion says that the force F acting on the object is equal to its mass m times its acceleration a. What is the resulting acceleration of the object?

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In Example 1.1.1 we found that the net force being applied to the object is [latex]\vec{F}=\left [ \begin{matrix} 200 \ 50\sqrt{3} \end{matrix} ight ] [/latex]. The total amount of force being applied will be the length of this vector:

[latex]\left\|\vec{F} ight\| =\sqrt{(200)^{2}+(50\sqrt{3})^{2} }\ =\sqrt{47500} \\approx 218[/latex]

Hence, the total amount of force is about F = 218 N. Thus, we find that the acceleration is approximately

[latex]a=\frac{F}{m}=\frac{218}{10}=21.8m/s^{2} [/latex]

Question 1.3.1: An object that weighs 10kg is being pulled by two strings wi...

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