A 4.0kg laboratory cart sits at rest on a level, frictionless track. Four horizontal forces act on the cart, as listed below, and a fifth unknown horizontal force F5 is also applied so that the cart remains at rest.
1. F1=12N directed 50∘ north of east
2. F2=9.0N directed due west
3. F3=6.0N directed 30∘ south of east
4. F4=4.0N directed due south
Answer the following in sequence.
(a) Resolve each of the four known forces into its north–south and east–west components. Organize your results in a table.
(b) Determine the magnitude and direction of the unknown force F5 that must be applied to keep the cart in translational equilibrium. Express the direction as an angle measured counterclockwise from due east.
(c) Demonstrate explicitly that the complete set of five forces produces zero net force on the cart.
(d) If F2 were increased to 12N while all other forces (including F5 from part (b)) remained unchanged, predict qualitatively the subsequent motion of the cart. Justify your prediction without performing additional calculations.