A horse is towing a canal boat, the tow rope making an angle of 10 o with the tow path. If the tension
in the rope is 20N, how many joules of work are done while moving 50m along the tow path?
F = 20*cos10 = 19.7 N.
W = F*d = 19.7*50 = ___ Joules.
Well, I must say, that's quite the dynamic duo - a horse and a canal boat! Let's see if we can calculate the amount of work being done.
The work done is given by the formula W = F × d × cos(theta), where W is the work done, F is the force applied, d is the displacement, and theta is the angle between the force and the displacement.
In this case, the force is given as 20N, the displacement is 50m, and the angle theta is 10 degrees. We just need to do a bit of trigonometry to find the value of cos(theta).
Using a handy-dandy calculator, we find that cos(10 degrees) is approximately 0.9848.
Now, let's plug the values into the formula:
W = 20N × 50m × 0.9848
Calculating this out gives us:
W ≈ 984.8 joules
So, it looks like approximately 984.8 joules of work are done while moving 50m along the tow path.
Now, I hope that explanation wasn't too "horse-playful" for you!
To determine the work done while moving the canal boat, we need to calculate the component of the force acting in the direction of motion and then multiply it by the distance moved.
Given:
Force, F = 20 N
Angle, θ = 10 degrees
Distance, d = 50 m
First, we need to find the component of the force in the direction of motion. This can be done by multiplying the force by the cosine of the angle.
Component of Force = Force * cos(θ)
Component of Force = 20 N * cos(10 degrees)
Component of Force ≈ 20 N * 0.9848
Component of Force ≈ 19.696 N (rounded to three decimal places)
Now, we can calculate the work done:
Work done = Component of Force * Distance
Work done = 19.696 N * 50 m
Work done ≈ 984.8 joules
Therefore, approximately 984.8 joules of work are done while moving 50 m along the tow path.
To determine the work done while towing the canal boat, we can use the formula:
Work = Force × Distance × cos(angle)
where:
- Work is the amount of energy transferred or expended in performing the task (measured in joules, J),
- Force is the force exerted in the direction of the displacement (measured in newtons, N),
- Distance is the distance traveled in the direction of the applied force (measured in meters, m), and
- Angle is the angle between the force vector and the displacement vector (measured in degrees).
In this case, the tension in the rope is the force exerted by the horse, which is 20N. The distance traveled along the tow path is given as 50m. The angle between the tow rope and the tow path is 10°.
Plugging these values into the formula, we have:
Work = 20N × 50m × cos(10°)
To evaluate cos(10°), we can use a calculator or computer software. After calculating it, we can substitute the value into the equation to find the work done.