Final answer:
The formula for work when the force is opposite to displacement is W = Fd cos(θ), with θ=180°, resulting in negative work. For example, with a friction force opposite to the displacement, if a force of 5.00 N and a displacement of 0.800 m, the work done is -4.00 J.
Step-by-step explanation:
When the angle θ between the force vector and the displacement vector is 180°, this indicates that the force is acting in the direction opposite to the displacement. In physics, the formula for calculating work (W) done by a force over a certain displacement is W = Fd cos(θ). Given that cos(180°) = -1, the work done by the force is negative, meaning it is opposing the motion.
In the context of friction, where the friction force (Ffr) and displacement are in opposite directions, the work done by friction would be Wfr = -Ffrd. So, if a frictional force of 5.00 N is acting over a displacement of 0.800 m in the opposite direction, the work done by friction would be -4.00 J.
It's important to remember that work can also be zero or positive. It's zero if the displacement is perpendicular to the force or there is no displacement. Work is positive when the force and displacement are in the same direction, further indicating that energy is being transferred in the direction of the force.