Forces of 2.4 N and 1.8 N act on an object at right angles to one another. What is the magnitude of a third force acting on the same object so that it remains stationary?
A) 3.0 N
B) 4.2 N
C) 0.6 N
I don't understand how the answer is A)
equilibrant=-sqrt(2.4^2+1.8^2)
but if you have a keen eye, you recognize this as a 3,4,5 triangle, so the equilibrant is 30 (5*6), legs of triangle are 3*6, 4*6
oops, 3.0
To determine the magnitude of the third force needed for the object to remain stationary, we can use vector addition. Since the two forces are acting at right angles to each other, we can treat them as perpendicular components of a single resultant force.
Let's label the first force as F1 = 2.4 N and the second force as F2 = 1.8 N.
Using the Pythagorean theorem, we can calculate the magnitude of the resultant force (R):
R^2 = F1^2 + F2^2
R^2 = (2.4 N)^2 + (1.8 N)^2
R^2 = 5.76 N^2 + 3.24 N^2
R^2 = 9 N^2
Taking the square root of both sides, we find:
R = √9 N
R = 3 N
Therefore, the magnitude of the third force needed to keep the object stationary is 3 N. The correct answer is A) 3.0 N.
To understand how to find the magnitude of the third force, let's break down the problem step by step.
First, let's consider the forces acting on the object. We have two forces: a 2.4 N force (let's call it force A) and a 1.8 N force (let's call it force B). These two forces act at right angles to each other.
Now, let's think about what it means for the object to remain stationary. If the object is not moving, that means the net force acting on it is zero. In other words, the vector sum of the forces acting on the object should be zero.
To find the magnitude of the third force that will keep the object stationary, we need to find a force that, when added to forces A and B, will result in a net force of zero.
Now, let's apply some basic vector addition. Since forces A and B act at right angles, we can add them together using the Pythagorean theorem. The magnitude of the resultant force (let's call it force C) is given by:
|C| = sqrt(A^2 + B^2)
Plugging in the values, we get:
|C| = sqrt((2.4 N)^2 + (1.8 N)^2)
= sqrt(5.76 N^2 + 3.24 N^2)
= sqrt(9 N^2)
= 3 N
So, the magnitude of the third force, force C, is 3 N.
Thus, the answer is A) 3.0 N.