a sailor pulls a boat along a dock by a rope held at an angle of 55.5 with the horizontal. How much work is done if the sailor exerts a force of 345 N on the rope and pulls the boat 23.8 m?
work= force*distance*cosAngle
The problem here is you gave the angle with respect to the horizontal. In what direction did the boat move?
To find the work done by the sailor, we can use the formula:
Work = Force * Distance * cos(angle)
Given:
Force = 345 N
Distance = 23.8 m
Angle = 55.5 degrees
First, we need to convert the angle from degrees to radians:
Angle (in radians) = Angle (in degrees) * pi / 180
Angle (in radians) = 55.5 * pi / 180
Angle (in radians) ≈ 0.9695 radians
Now, we can calculate the work done:
Work = 345 N * 23.8 m * cos(0.9695 radians)
Using a calculator, we find that cos(0.9695 radians) ≈ 0.5513
Work ≈ 345 N * 23.8 m * 0.5513
Work ≈ 4375.115 N·m
Therefore, the work done by the sailor is approximately 4375.115 N·m.
To calculate the work done by the sailor, you need to use the formula:
Work = Force × Distance × cos(θ),
where Force is the magnitude of the force applied, Distance is the distance moved, and θ is the angle between the force and the direction of movement.
In this case, the sailor exerts a force of 345 N and pulls the boat a distance of 23.8 m. The angle θ is given as 55.5°.
First, convert the angle from degrees to radians:
θ = 55.5° × (π/180) ≈ 0.969 rad.
Now, substitute the values into the work formula:
Work = 345 N × 23.8 m × cos(0.969 rad).
Using a calculator, compute the value of cos(0.969 rad) to find the final answer.