Question

Exactly three forces act on an object: 12.0 Newtons to the North, 300 Newtons to the East, and 14.0 Newtons to the West. What is the magnitude and direction of the single force that could be added to the object to put it into equilibrium?

A) 12.0 N to the East
B) 300 N to the South
C) 14.0 N to the North
D) 316 N to the West

Answer 1

The magnitude of the single force needed to put the object into equilibrium is 18.4 N to the West.

Step-by-step explanation:

A free-body diagram would show a northward force of 12.0 N and a westward force of 14.0 N. In order for the object to be in equilibrium, the magnitude and direction of the single force that could be added must be equal to the sum of these forces but in the opposite direction. Using the Pythagorean theorem, we can calculate the magnitude of this force:

Magnitude = sqrt((12.0 N)^2 + (14.0 N)^2) = 18.4 N

Since the two forces are acting in opposite directions, the direction of the single force that will put the object in equilibrium is the same as the direction of the greater force, which is to the West.