Final answer:
In physics, the work done by friction when pushing a couch across a floor with constant velocity can be calculated using the coefficient of friction and the normal force, and power is the rate of doing work. This involves multiplying the coefficient of friction by the normal force and the displacement, and taking into account the movement's direction.
Step-by-step explanation:
The scenario you describe involves physics principles, specifically related to work and energy. When moving the couch across the floor at a constant velocity, the frictional force opposing the motion does work on the couch.
Calculating Work Done by Frictional Force
To calculate the work done by the frictional force, we apply the formula:
Work = Force x Distance x cos(θ)
Since the direction of friction is opposite to the direction of motion (cos(180°) = -1), and the force of friction (f) can be found by multiplying the coefficient of friction (μ) times the normal force (N), the formula becomes:
Work by friction = μ x N x displacement x (-1)
Given the normal force (1 kN) and coefficient of friction (0.6), we can calculate the work done by friction when the couch is pushed 3 m parallel and then 1 m perpendicular to the wall. Remember, the distance here is the total displacement during the whole movement.
Total Work Against Friction
When the couch is moved back to its original position, we would calculate the work done against friction over the entire round trip. Since the work done by friction is a path-dependent process, the total work would be the sum of work for each segment, which would essentially double the value calculated for one way (assuming the same path is followed back).
Do not forget that power is the rate of doing work. If you slide the couch across the floor and want to calculate the power expended, you will use the formula:
Power = Work / Time