Question

Nancy and Harry are sliding a stone statue and moving it to a new location in their garden. Nancy is pushing the statue with a force of 120N at a 60° angle to the horizontal and Harry is pulling the statue with a force of 180N at a 40° angle with the horizontal. What is the magnitude of the horizontal force exerted on the statue?

Answer 1

To find the magnitude of the horizontal force exerted on the statue, we need to resolve the forces applied by Nancy and Harry into their horizontal components. Nancy's horizontal force is 60N and Harry's horizontal force is 137.48N. The magnitude of the horizontal force exerted on the statue is 197.48N.

Step-by-step explanation:

To find the magnitude of the horizontal force exerted on the statue, we need to resolve the forces applied by Nancy and Harry into their horizontal components.

Nancy is pushing the statue with a force of 120N at a 60° angle to the horizontal, so the horizontal component of her force is 120N * cos(60°) = 60N.

Harry is pulling the statue with a force of 180N at a 40° angle with the horizontal, so the horizontal component of his force is 180N * cos(40°) = 137.48N.

To find the magnitude of the horizontal force exerted on the statue, we sum up the horizontal components of both forces: 60N + 137.48N = 197.48N.

Answer 2

197,8879 N.

Step-by-step explanation:

The magnitude of the horizontal force exerted on the statue can be calculated using trigonometric functions.

The question given says that Nancy is pushing the statue with a force of 120 N at a 60° angle to the horizontal and Harry is pulling the statue with a force of 180 N at a 40° angle with the horizontal.

With that information can be calculated the horizontal force exerted on the statue by Nancy, the horizontal force exerted on the statue by Harry and, adding that results, the total horizontal magnitude can be calculated.

The cosine function can be used to calculate the horizontal component of the forces exerted by Nancy and Harry, to determine the horizontal component of the force exerted on the statue.

F= (120 N cos 60°) + (180 N x cos 40°)

F= 197,8879 N