Question

A man cleaning his apartment pushes a vacuum cleaner with a force of magnitude 84.5 N. The force makes an angle of 33.9 ◦ with the horizontal floor. The vacuum cleaner is pushed 2.62 m to the right along the floor. Calculate the work done by the 84.5 N force.

Answer 1

The work done by the man pushing the vacuum cleaner with a force of 84.5 N at an angle of 33.9° over a distance of 2.62 m is approximately 184.8 joules.

Step-by-step explanation:

To calculate the work done by a force, you can use the formula W = F × d × cos(θ), where W is the work done, F is the magnitude of the force, d is the distance the object moves, and θ is the angle the force makes with the horizontal direction of movement. In this case, the man pushes a vacuum cleaner with a force of 84.5 N at an angle of 33.9° over a distance of 2.62 m. We multiply the force by the distance and the cosine of the angle to find:

W = 84.5 N × 2.62 m × cos(33.9°)

Calculating cosine of 33.9 degrees and multiplying with the force and distance, we get:

W = 84.5 × 2.62 × 0.8326 ≈(joules)

The man does approximately 184.8 joules of work pushing the vacuum cleaner.

Answer 2

183.75641 Joules

Step-by-step explanation:

F = Force of the vacuum cleaner = 84.5 N

s = Displacement of the vacuum cleaner = 2.62 m

`\theta` = Angle the force makes with the horizontal = 33.9°

Work done is given by

`W=F* scos\theta\\\Rightarrow W=84.5* 2.62* cos33.9\\\Rightarrow W=183.75641\ J`

The work done by the force of the vacuum cleaner is 183.75641 Joules