Final answer:
Emily does a total of 495 joules of work on the painting, with 450 joules from horizontally carrying it 15 meters and 45 joules from lifting it 1.5 meters up the stairs.
Step-by-step explanation:
In order to find out how much work Emily does on the painting, we need to consider the work done in both carrying the painting horizontally and lifting it vertically. The formula for work is given by work (W) = force (F) × distance (d) × cos(θ), where θ is the angle between the force direction and the direction of motion. When Emily carries the painting 15 m on a level sidewalk, the force direction and the motion direction are the same (0 degrees), so the work done is simply:
W_horizontal = 30 N × 15 m × cos(0°) = 450 J.
Next, we look at Emily carrying the painting up the stairs. Since she climbs 1.5 m, and the force exerted is in the same direction as the motion (vertically upwards), the work done here is:
W_vertical = 30 N × 1.5 m × cos(0°) = 45 J.
The total work done by Emily is therefore the sum of these two:
Total work = W_horizontal + W_vertical = 450 J + 45 J = 495 J.
Note that the time taken to do the work is not relevant in this calculation, as work is a measure of energy transfer and not power, which involves time.