Two horses pull horizontally on ropes attached to a tree stump (Fig. 3). Each horse pulls with a force of magnitude F. If the angle between the two ropes is 126O, what is the resultant force?
Fr = F[0o] + F[126o] =
F + F*Cos126 + (F*sin126)i =
F - 0.588F + 0.809Fi=0.412F + 0.809i.
Tan A = 0.809F/0.412F = 1.96359.
A = 63o N. of E. = 63o CCW.
Fr = 0.809F/sin63 = 0.908F[63o]
Explain
Two horses pull horizontally on ropes attached to a tree stump . Each horse pulls with a force of magnitude F. If the angle between the two ropes is 126O, what is the resultant force?
To find the resultant force, we need to consider the forces exerted by each horse and their direction. Given that each horse pulls with a force of magnitude F, we can visualize the forces as vectors.
In this case, we have two forces acting in different directions. Let's denote the angle between the ropes as θ. Since the angle between the ropes is given as 126 degrees, we can substitute θ = 126°.
Now, to find the resultant force, we can use vector addition. We'll need to break down the forces into their horizontal and vertical components.
Since the horses are pulling horizontally, there is no vertical component to consider. Thus, we only need to add the horizontal components of the forces.
To find the horizontal component of each force, we can use trigonometry. As the forces are horizontally oriented, both horizontal components are equal to F*cos(θ).
So, the horizontal components of both forces are F*cos(126°) and F*cos(126°).
Now, we can add the horizontal components of the forces to find the resultant force:
Resultant force = F*cos(126°) + F*cos(126°)
Simplifying this expression, we have:
Resultant force = 2*F*cos(126°)
Therefore, the resultant force is 2*F*cos(126°).