Question

A barge is hauled along a straight-line section of canal by two horses harnessed to tow ropes and walked along the tow paths on either side of the canal. Each horse pulls with a force of 504 N at an angle of 17° with the centerline of the canal. Find the net force on the barge, in kilonewtons.

Answer 1

To find the net force on the barge, resolve the forces exerted by the horses into their x and y components. Add the x-components together and the y-components together to find the resultant force. Use the Pythagorean theorem to find the magnitude of the resultant force and trigonometry to find the direction.

Step-by-step explanation:

The net force on the barge can be found by resolving the forces exerted by the horses into their x and y components. The force exerted by each horse can be split into two vectors: one in the x-direction and one in the y-direction. Since the angle between the force and the centerline of the canal is given, we can use trigonometry to find the x and y components.

The x-component of the force exerted by each horse can be found by multiplying the force by the cosine of the angle. The y-component can be found by multiplying the force by the sine of the angle. We will have two x-components and two y-components.

To find the net force on the barge, we need to add the x-components together and the y-components together. The resultant force will be the sum of the x-components and the sum of the y-components. We can use the Pythagorean theorem to find the magnitude of the resultant force, and we can use trigonometry to find the direction.