Question

A chain is attached to a boulder and pulled due north by a monster truck with a force of magnitude 2044 newtons. (A newton is about a quarter of a pound.) A second monster truck pulls on a chain pointed 20° west of north with a force of magnitude 3045 newtons. Find the resultant force on the boulder and its direction. (Use decimal notation. Give your answer for the force to one decimal place. Give your answer for the direction of the boulder to the nearest degree. Include the degree symbol in your answer where needed.) Calculate resultant force in newtons and the resultant direction in degrees West of North

Answer 1

So, the resultant force on the boulder is 4968.1 N and its direction is 12° west of north. Please check the explanation below to help you remember the steps.

Explanation:

The resultant force can be found by adding the two forces vectorially.

The force from the first truck (F1) is 2044 N due north.

The force from the second truck (F2) can be broken down into its northward and westward components. The northward component (F2n) is F2*cos(20°) = 3045*cos(20°) = 2851.6 N. The westward component (F2w) is F2*sin(20°) = 3045*sin(20°) = 1043.5 N.

The total northward force (Fn) is F1 + F2n = 2044 + 2851.6 = 4895.6 N.

The total westward force (Fw) is F2w = 1043.5 N.

The magnitude of the resultant force (Fr) can be found using the Pythagorean theorem: Fr = √(Fn^2 + Fw^2) = √(4895.6^2 + 1043.5^2) = 4968.1 N.

The direction of the resultant force (θ) can be found using the arctangent function: θ = arctan(Fw/Fn) = arctan(1043.5/4895.6) = 12° west of north.

So, the resultant force on the boulder is 4968.1 N and its direction is 12° west of north.