Serway & Jewett — Energy of a System: Problem 45.

Review. Two constant forces act on an object of mass \(m = 5.00 \text{ kg}\) moving in the \(xy\) plane as shown in Figure P7.45. Force \(\vec{F}_1\) is \(25.0 \text{ N}\) at \(35.0^\circ\), and force \(\vec{F}_2\) is \(42.0 \text{ N}\) at \(150^\circ\). At time \(t = 0\), the object is at the origin and has velocity \((4.00 \hat{i} + 2.50 \hat{j}) \text{ m/s}\). (a) Express the two forces in unit-vector notation. Use unit-vector notation for your other answers. (b) Find the total force exerted on the object. (c) Find the object's acceleration. Now, considering the instant \(t = 3.00 \text{ s}\), find (d) the object's velocity, (e) its position, (f) its kinetic energy from \(\frac{1}{2}mv_f^2\), and (g) its kinetic energy from \(\frac{1}{2}m v_i^2 + \sum \vec{F} \cdot \Delta\vec{r}\). (h) What conclusion can you draw by comparing the answers to parts (f) and (g)?