A force is applied to a 2.0-kg, radio-controlled model car parallel to the x-axis as it moves along a straight track. The x- component of the force varies with the x-coordinate of the car (?Fig. E6.43?). Calculate the work done by the force when the car moves from (a) x = 0 to x = 3.0 m; (b) x = 3.0 m to x = 4.0 m; (c) x = x = 4.0 m to x = 7.0 m; (d) x = 0 to x = 7.0 m; (e) x = 7.0 m to x = 2.0 m.

Solution 41E Step 1 of 6: The magnitude of the work done by F equalsxthe area under the F versus x cxrve. The work is positive when F and xhe displacement are in the same direction; it is negative when they are in opposite directions. Step 2 of 6: a) Fxis positive and displacement x is positive, so w > 0 W = Area of the triangle + Area of the rectangle W = (22N × 2 m) + 2 N × 1 m = 4 J Step 3 of 6:: b) During this displacement F = 0,xso W = 0