how much work is done on a vacuum cleaner pulled 5.0m by a force of 45.0 N at an angle 35 above the horizintal? solving work
To solve for the work done on a vacuum cleaner, we need to use the formula:
Work = Force * Distance * cos(angle)
Given:
Force = 45.0 N
Distance = 5.0 m
Angle = 35 degrees
First, we need to convert the angle from degrees to radians:
angle_radians = angle * (π/180)
angle_radians = 35 * (π/180)
angle_radians ≈ 0.6109 radians
Now, we can substitute the given values into the work formula:
Work = 45.0 N * 5.0 m * cos(0.6109)
Using a calculator, we can find the value of cos(0.6109) ≈ 0.803
Work ≈ 45.0 N * 5.0 m * 0.803
Calculating further:
Work ≈ 180.15 N*m
Therefore, the work done on the vacuum cleaner is approximately 180.15 N*m.
To solve the work done, we need to use the formula:
Work = Force * Distance * cos(theta),
where:
- Work is the amount of work done,
- Force is the applied force,
- Distance is the displacement, and
- Theta is the angle between the force and the direction of displacement.
In this case, we are given:
- Force = 45.0 N,
- Distance = 5.0 m, and
- Theta = 35 degrees.
Let's plug in these values into the work formula to calculate the work done:
Work = 45.0 N * 5.0 m * cos(35 degrees).
Now, let's calculate the cosine of 35 degrees:
cos(35 degrees) ≈ 0.819.
Plugging this value back into the formula:
Work ≈ 45.0 N * 5.0 m * 0.819.
Now, we can calculate the work done:
Work ≈ 183.7 joules.
Therefore, approximately 183.7 joules of work is done on the vacuum cleaner.