Tension

[Dominic]

An 800-kg car is being towed with a constant speed along a slope. What is the tension in the cable? Neglect all resistive forces. The slope it is on is 20 degrees and the angle that the truck is towing at is 30 degrees.

[HallsofIvy]

The roadway is supporting part of the weight of the car- the component of the "weight vector" perpendicular to the roadway. If the roadway were flat, that would be the entire weight and there would be tension in the cable only when accelerating. Since the roadway is at 20 degrees, take the weight of the car (downward) and find components perpendicular to and parallel to the roadway. The cable has to support the component parallel to the roadway.

The force parallel to the road way is one leg of a right triangle with the tow cable as hypotenuse. Since you know the angle is 30 degrees, you can calculate the "length of the hypotenuse" (the tension in the cable).