Two workhorses tow a barge along a straight canal. Each horse exerts a constant force of magnitude F, and the tow ropes make an angle θ with the direction of motion of the horses and the barge. (Figure 1) Each horse is traveling at a constant speed v.
How much work W is done by each horse in a time t?
Express the work in terms of the quantities given in the problem introduction.
How much power P does each horse provide?
Express your answer in terms of the quantities given in the problem introduction.
A = Theta.
W = (F*cosA) * V*t.
P = (F*cosA) * V
W = (Fcos(theta))*vt
To determine the amount of work done by each horse in a time t, we need to calculate the work done by a single horse pulling the barge.
First, we need to consider the work done by a single horse. The work done by a force F acting through a displacement s can be calculated using the equation:
Work (W) = force (F) × displacement (s) × cosine of the angle between the force and displacement (θ)
In this case, the displacement of the barge in time t will be equal to the speed of the horse (v) multiplied by the time (t):
Displacement (s) = v × t
Substituting this value into the formula for work, we get:
Work (W) = F × v × t × cosine(θ)
Thus, the work done by each horse in time t is F × v × t × cosine(θ).
To calculate the power (P) provided by each horse, we need to divide the work done (W) by the time taken (t):
Power (P) = Work (W) / Time (t)
Substituting the equation for work into the equation for power, we get:
Power (P) = (F × v × t × cosine(θ)) / t
Simplifying the equation, the time (t) cancels out:
Power (P) = F × v × cosine(θ)
Therefore, each horse provides a power of F × v × cosine(θ).