A 14.8 kg box is being dragged 12.5 m across the floor using a rope held at a 32 degree angle from the floor. the force being used is 146 N. Determine the work that has been done.
146 N*cos32*12.5 m = ___ J
To determine the work that has been done, we can use the formula:
Work = Force × Distance × cos(θ)
Where:
- Work is the amount of work done (in joules, J)
- Force is the applied force (in newtons, N)
- Distance is the distance over which the force is applied (in meters, m)
- θ is the angle between the force and the displacement vector (in degrees)
In the given problem:
- Force (F) = 146 N
- Distance (d) = 12.5 m
- Angle (θ) = 32 degrees
First, let's convert the angle from degrees to radians:
θ_radians = θ × (π/180)
θ_radians = 32 × (π/180)
θ_radians ≈ 0.5585 radians
Now, substitute the values into the formula:
Work = 146 N × 12.5 m × cos(0.5585)
Calculate the value of cos(0.5585) using a calculator or a math software:
cos(0.5585) ≈ 0.8702
Now, substitute the value of cos(0.5585) back into the formula and calculate the work:
Work ≈ 146 N × 12.5 m × 0.8702
Calculate the final value:
Work ≈ 1770.725 J
Therefore, the work done is approximately 1770.725 joules.