How much work is done on a vacuum cleaner pulled 3m by a force of 50N at a angle of 30° with the horizontal?
To determine the work done on a vacuum cleaner being pulled, you can use the formula:
Work = Force x Distance x cosθ
Where:
- Work is measured in joules (J),
- Force is measured in newtons (N),
- Distance is measured in meters (m),
- θ (theta) is the angle between the force and the direction of motion.
In this case, the force is 50 N, and the distance is 3 m. The angle θ is 30°.
So, let me calculate the work done for you:
Work = 50 N x 3 m x cos(30°)
Before we continue, note that the cosine function in most calculators expects angles to be in radians. So, we need to convert 30° to radians:
θ (in radians) = θ (in degrees) x π / 180
θ (in radians) = 30° x π / 180
θ (in radians) = (30π) / 180
θ (in radians) = π / 6
Now we can continue with the calculation:
Work = 50 N x 3 m x cos(π / 6)
Using a scientific calculator or calculator software, calculate the cosine of π / 6:
cos(π / 6) ≈ 0.866
Now substitute this value back into the equation:
Work = 50 N x 3 m x 0.866
Work ≈ 130 J
Therefore, the work done on the vacuum cleaner is approximately 130 joules (J) when it is pulled 3 m by a force of 50 N at an angle of 30° with the horizontal.