A barge is hauled along a straight-line section of canal by two horses harnessed to tow ropes and walking along the tow paths on either side of the canal. Each horse pulls with a force of 540 N at an angle of 12° with the centerline of the canal. What is the net force on the barge?
2*540*cos12 = ____ N
911.36
To find the net force on the barge, we need to determine the horizontal and vertical components of the force exerted by each horse. We can then add up these components to find the net force.
First, let's find the horizontal component of the force exerted by each horse. We can determine this by multiplying the magnitude of the force by the cosine of the angle it makes with the centerline of the canal.
Horizontal component of force = Force × cos(angle)
For each horse:
Horizontal component of force = 540 N × cos(12°)
Next, let's find the vertical component of the force exerted by each horse. We can determine this by multiplying the magnitude of the force by the sine of the angle it makes with the centerline of the canal.
Vertical component of force = Force × sin(angle)
For each horse:
Vertical component of force = 540 N × sin(12°)
Now, we can add up the horizontal and vertical components of the force exerted by each horse to find the net force on the barge. Since the horses are walking along the tow paths on either side of the canal, the horizontal components will cancel out, leaving only the vertical components to contribute to the net force.
Net force on the barge = (Vertical component of force for horse 1) + (Vertical component of force for horse 2)
Net force on the barge = 2 × (540 N × sin(12°))
Calculate the value to find the net force on the barge.