Understanding Collinear Forces

Oct 13, 2025 by wbrum.org 137 views

Introduction

In physics, forces are vectors that can be represented graphically as arrows. When two forces act in opposite directions, they are said to be collinear. In this article, we will explore the concept of collinear forces and how to find the resultant force when they act in opposite directions and at right angles to each other.

Understanding Collinear Forces

Collinear forces are forces that act in the same direction or in opposite directions. When two forces act in opposite directions, they are said to be collinear and opposite. The resultant force of two collinear forces acting in opposite directions is the difference between the magnitudes of the two forces.

Mathematical Representation

Let's represent the two collinear forces as vectors P and Q. When they act in opposite directions, the resultant force R is given by:

R = P - Q

When they act at right angles to each other, the resultant force R is given by:

R = √(P^2 + Q^2)

Given Information

We are given that when P and Q act in opposite directions, their resultant force R is 34 N. We are also given that when they act at right angles to each other, their resultant force R is 550 N.

Equations

We can write two equations based on the given information:

P - Q = 34 ... (Equation 1)
√(P^2 + Q^2) = 550 ... (Equation 2)

Solving the Equations

We can solve these equations simultaneously to find the values of P and Q.

Step 1: Square Equation 1

Squaring Equation 1, we get:

(P - Q)^2 = 34^2 P^2 - 2PQ + Q^2 = 1156

Step 2: Substitute into Equation 2

Substituting P^2 - 2PQ + Q^2 from Step 1 into Equation 2, we get:

√(P^2 - 2PQ + Q^2) = 550 P^2 - 2PQ + Q^2 = 302500

Step 3: Equate the Two Equations

Equating the two equations from Step 1 and Step 2, we get:

P^2 - 2PQ + Q^2 = 302500 P^2 - 2PQ + Q^2 = 1156

Step 4: Solve for P and Q

Subtracting the two equations from Step 3, we get:

0 = 301344 -2PQ = 301344

Dividing both sides by -2, we get:

PQ = -150672

Step 5: Find the Values of P and Q

We can now find the values of P and Q by substituting PQ = -150672 into Equation 1:

P - Q = 34 P + 150672 = 34 + Q P = -150638

Substituting P = -150638 into PQ = -150672, we get:

Q = -150638 + 34 Q = -150604

Conclusion

In this article, we have explored the concept of collinear forces and how to find the resultant force when they act in opposite directions and at right angles to each other. We have also solved the equations to find the values of P and Q.

Final Answer

The final answer is:

P = -150638 N Q = -150604 N

Note

Introduction

In our previous article, we explored the concept of collinear forces and how to find the resultant force when they act in opposite directions and at right angles to each other. We also solved the equations to find the values of P and Q. In this article, we will answer some frequently asked questions related to collinear forces.

Q&A

Q: What are collinear forces?

A: Collinear forces are forces that act in the same direction or in opposite directions.

Q: What is the resultant force of two collinear forces acting in opposite directions?

A: The resultant force of two collinear forces acting in opposite directions is the difference between the magnitudes of the two forces.

Q: How do we find the resultant force of two collinear forces acting at right angles to each other?

A: We can find the resultant force of two collinear forces acting at right angles to each other by using the Pythagorean theorem: R = √(P^2 + Q^2)

Q: What is the difference between collinear forces and parallel forces?

A: Collinear forces are forces that act in the same direction or in opposite directions, while parallel forces are forces that act in the same direction but are not necessarily collinear.

Q: Can we have three collinear forces acting in opposite directions?

A: Yes, we can have three collinear forces acting in opposite directions. However, the resultant force will be the difference between the magnitudes of the two forces that are not in the same direction.

Q: How do we find the resultant force of three collinear forces acting in opposite directions?

A: We can find the resultant force of three collinear forces acting in opposite directions by using the following equation: R = P - Q - R'

where R' is the resultant force of the two forces that are not in the same direction.

Q: Can we have four collinear forces acting in opposite directions?

A: Yes, we can have four collinear forces acting in opposite directions. However, the resultant force will be the difference between the magnitudes of the two forces that are not in the same direction.

Q: How do we find the resultant force of four collinear forces acting in opposite directions?

A: We can find the resultant force of four collinear forces acting in opposite directions by using the following equation: R = P - Q - R' - R''

where R' and R'' are the resultant forces of the two forces that are not in the same direction.

Conclusion

In this article, we have answered some frequently asked questions related to collinear forces. We have also provided examples of how to find the resultant force of two, three, and four collinear forces acting in opposite directions.

Final Answer

The final answer is:

Collinear forces are forces that act in the same direction or in opposite directions.
The resultant force of two collinear forces acting in opposite directions is the difference between the magnitudes of the two forces.
We can find the resultant force of two collinear forces acting at right angles to each other by using the Pythagorean theorem: R = √(P^2 + Q^2)
We can have three and four collinear forces acting in opposite directions, and we can find the resultant force by using the following equations: R = P - Q - R' and R = P - Q - R' - R''