Final answer:
The work done on a vacuum cleaner when pulled 4.5 m by a force of 35.0 N at an angle of 38° above the horizontal is approximately 123.93 Joules. We find this by calculating the parallel component of the force using the cosine of the angle and then multiplying by the distance.
Step-by-step explanation:
To calculate the work done on a vacuum cleaner pulled at an angle, we use the formula Work (W) = Force (F) × Distance (d) × cos(θ), where θ is the angle between the force direction and the direction of movement. Here, the force is 35.0 N, the distance is 4.5 m, and the angle is 38° above the horizontal. Since the force is at an angle, we only consider the component of the force that is parallel to the direction of displacement.
To find the parallel component of the force, we multiply the force by the cosine of the angle. So, the parallel component of the force (Fparallel) is 35.0 N × cos(38°). Then we multiply this by the distance to find the work done:
W = Fparallel × d = 35.0 N × cos(38°) × 4.5 m.
Plugging in the values and calculating, we get:
W = 35.0 N × cos(38°) × 4.5 m
≈ 35.0 N × 0.7880 × 4.5 m
≈ 123.93 Joules.
Therefore, the work done on the vacuum cleaner is approximately 123.93 Joules.