4. A 350-kg box initially at rest is pulled 7.00 m up a 30.0" inclined plane by an external force PM = 5.00 X 103 N that is exerted parallel to the plane. Assume friction is negligible. a. Construct a representation of the scenario that includes the ramp, the inclination of the ramp, the external force exerted on the box, the displacement, the box, and the coordinate system to be used for the analysis of the problem. Represent each characteristic with a label that will be used in an analysis. b. Construct a free-body diagram for the box. c. Construct a diagram representing the decomposition of the gravitational force into components parallel and perpendicularto the ramp. One ofthe angles in your vector diagram will be the same as the angle of inclination of the ramp. Mark this angle on your vector diagram. Add the displacement vector to this diagram and mark the angle, ta ken to be positive in the counterclockwise direction, between the displacement vector and the gravitational force vector, to your diagram. d. Express the components of the gravitational force along the ramp and perpendicularto the ramp in terms of F3 and 0. e. Express the work done on the box by the gravitational force in terms of 6. Hint: To be sure of your expression you can use the trigonometric identity cos(a ,8) = (203(1):) 005(3) + sin(a) sin() to express the work done on the box by the gravitational force. f. Apply the object model to the box and express the final kinetic energy of the box in terms of the work done on the box by the external force and the gravitational field. g. Consider the Ea rthbox system and apply energy conservation to express the final kinetic energy in terms of the work done by the external force and the change in gravitational potential energy of the Ea rthbox system. h. Compare the expressions from parts (f) and (g) and explain similarities and differences. i. Calculate the final speed of the box