Answer to Question #214608 in Physics for Kayla

Question

A 5.0 kg toolbox is pulled west across a concrete floor with a rope. The rope makes an angle of 45.0° with the floor. A force of 85.0 N is exerted on the rope, and the force of friction is 15.0 N parallel to the floor. The magnitude of the acceleration of the box is ___m/s^2.(give your answer with the correct number of signification digits and do not include units in your answer)

Note:Let West be positive.

Answer 1

Let's apply the Newton's Second Law of Motion:

$$Fcos\theta-F_{fr}=ma,$$ $$a=\dfrac{Fcos\theta-F_{fr}}{m},$$ $$a=\dfrac{85\ N\cdot cos45^{\circ}-15\ N}{5\ kg}=9.0\ \dfrac{m}{s^2}.$$