A horse tows a barge in a canal by means of a rope that makes an angle of 15 degrees with the direction of motion of the barge. The tension in the rope is 120 N. How much work is done in moving the barge 1000 m?
To calculate the work done in moving the barge, we can use the formula:
Work = Force × Distance × cos(θ)
where
- Work is the amount of work done (in joules or Newton-meters),
- Force is the tension in the rope (in newtons),
- Distance is the distance the barge is moved (in meters), and
- θ (theta) is the angle between the force and the direction of motion in radians.
Given that the tension in the rope is 120 N, the distance moved is 1000 m, and the angle is 15 degrees, we can substitute these values into the formula:
Work = 120 N × 1000 m × cos(15 degrees)
First, we need to convert the angle from degrees to radians:
θ (in radians) = θ (in degrees) × (π/180)
θ (in radians) = 15 degrees × (π/180)
θ (in radians) = 0.2618 radians
Now, we can calculate the work:
Work = 120 N × 1000 m × cos(0.2618 radians)
Work = 120,000 joules
Therefore, the amount of work done in moving the barge 1000 m is 120,000 joules.