Two horses are pulling a barge with a mass 2000 kg along a canal. the cable connected to the first horse makes an angle of θ1= 40 o with respect to the direction of the canal, while the cable connected to the second horse makes an angle of θ2= -20o . find the acceleration of the barge (magnitude and direction), starting at rest, if each horse exerts a force of magnitude 600 n. ignore forces of resistance.

a = 0.5195 m/s²

θ = 9.997º ≈ 10º

Explanation:

We apply Newton's 2nd Law as follows:

∑ Fx = m*ax

∑ Fy = m*ay

Then we have

∑ Fx = F₁x + F₂x = m*ax    ⇒ 600*Cos 40º + 600*Cos (-20º) = 2000*ax

⇒   ax = 0.5117 m/s²

∑ Fy = F₁y + F₂y = m*ay    ⇒ 600*Sin 40º + 600*Sin (-20º) = 2000*ay

⇒   ay = 0.0902 m/s²

the magnitude of the acceleration of the barge is

a = √(ax² + ay²) = √((0.5117 m/s²)² + (0.0902 m/s²))= 0.5196 m/s²

and the direction is

θ = Arctan (ay / ax) = Arctan (0.0902 / 0.5117) = 9.997º ≈ 10º