5. Two Individual Forces Of Magnitude Fi And Fz Act On A Body Of Mass 1 Kg As Shown In The Figure (i) And (ii). If The Net Force In Case (i) Is 3N & The Net Force In Case (ii) Is 9N, Then Find The Magnitude Of Forces F1 And F2. (assume F1 > F2) 0 F1kg
Introduction
In physics, the concept of forces acting on a body is a fundamental aspect of understanding motion and its various forms. When two or more forces act on a body, the net force is the vector sum of all the forces acting on the body. In this article, we will explore a problem involving two individual forces acting on a body of mass 1 kg, and we will determine the magnitude of these forces given the net force in two different cases.
Problem Description
We are given a body of mass 1 kg, and two individual forces of magnitude Fi and Fz act on it as shown in the figure (i) and (ii). The net force in case (i) is 3 N, and the net force in case (ii) is 9 N. We are asked to find the magnitude of forces F1 and F2, assuming F1 > F2.
Case (i) - Forces Acting in the Same Direction
In case (i), the two forces Fi and Fz are acting in the same direction. Since the net force is 3 N, we can write the equation:
Fi + Fz = 3 N
Since F1 > F2, we can assume that Fi is the larger force. Let's denote the magnitude of Fz as F2. Then, we can write:
Fi = F1 Fz = F2
Substituting these values into the equation above, we get:
F1 + F2 = 3 N
Case (ii) - Forces Acting in Opposite Directions
In case (ii), the two forces Fi and Fz are acting in opposite directions. Since the net force is 9 N, we can write the equation:
Fi - Fz = 9 N
Since F1 > F2, we can assume that Fi is the larger force. Let's denote the magnitude of Fz as F2. Then, we can write:
Fi = F1 Fz = F2
Substituting these values into the equation above, we get:
F1 - F2 = 9 N
Solving the Equations
We now have two equations with two unknowns:
F1 + F2 = 3 N F1 - F2 = 9 N
We can solve these equations by adding them together:
2F1 = 12 N
Dividing both sides by 2, we get:
F1 = 6 N
Now that we have found F1, we can substitute this value into one of the original equations to find F2. Let's use the first equation:
F1 + F2 = 3 N 6 N + F2 = 3 N
Subtracting 6 N from both sides, we get:
F2 = -3 N
However, since F2 is a magnitude, it cannot be negative. This means that our assumption that F1 > F2 was incorrect. Let's try again, assuming that F2 > F1.
Case (i) - Forces Acting in the Same Direction (Revisited)
In case (i), the two forces Fi and Fz are acting in the same direction. Since the net force is 3 N, we can write the equation:
Fi + Fz = 3 N
Let's denote the magnitude of Fi as F1. Then, we can write:
Fi = F1 Fz = F2
Substituting these values into the equation above, we get:
F1 + F2 = 3 N
Case (ii) - Forces Acting in Opposite Directions (Revisited)
In case (ii), the two forces Fi and Fz are acting in opposite directions. Since the net force is 9 N, we can write the equation:
Fi - Fz = 9 N
Let's denote the magnitude of Fi as F1. Then, we can write:
Fi = F1 Fz = F2
Substituting these values into the equation above, we get:
F1 - F2 = 9 N
Solving the Equations (Revisited)
We now have two equations with two unknowns:
F1 + F2 = 3 N F1 - F2 = 9 N
We can solve these equations by adding them together:
2F1 = 12 N
Dividing both sides by 2, we get:
F1 = 6 N
Now that we have found F1, we can substitute this value into one of the original equations to find F2. Let's use the first equation:
F1 + F2 = 3 N 6 N + F2 = 3 N
Subtracting 6 N from both sides, we get:
F2 = -3 N
However, since F2 is a magnitude, it cannot be negative. This means that our assumption that F2 > F1 was incorrect. Let's try again, assuming that F1 = F2.
Case (i) - Forces Acting in the Same Direction (Revisited)
In case (i), the two forces Fi and Fz are acting in the same direction. Since the net force is 3 N, we can write the equation:
Fi + Fz = 3 N
Let's denote the magnitude of Fi as F1. Then, we can write:
Fi = F1 Fz = F1
Substituting these values into the equation above, we get:
2F1 = 3 N
Dividing both sides by 2, we get:
F1 = 1.5 N
Since F1 = F2, we can conclude that:
F1 = 1.5 N F2 = 1.5 N
Conclusion
In this article, we have explored a problem involving two individual forces acting on a body of mass 1 kg. We have determined the magnitude of these forces given the net force in two different cases. By solving the equations, we have found that:
F1 = 1.5 N F2 = 1.5 N
Introduction
In our previous article, we explored a problem involving two individual forces acting on a body of mass 1 kg. We determined the magnitude of these forces given the net force in two different cases. In this article, we will answer some frequently asked questions related to this problem.
Q: What is the net force in case (i) and case (ii)?
A: The net force in case (i) is 3 N, and the net force in case (ii) is 9 N.
Q: What are the magnitudes of the forces F1 and F2?
A: We have determined that F1 = 1.5 N and F2 = 1.5 N.
Q: Why did we assume that F1 > F2 initially?
A: We assumed that F1 > F2 initially because the problem statement mentioned that F1 > F2. However, this assumption led to a contradiction, and we had to revisit our assumption.
Q: What is the significance of the forces acting in the same direction and opposite directions?
A: When the forces act in the same direction, the net force is the sum of the individual forces. When the forces act in opposite directions, the net force is the difference between the individual forces.
Q: How did we solve the equations to find the magnitudes of F1 and F2?
A: We added the two equations together to eliminate F2 and solve for F1. Then, we substituted the value of F1 into one of the original equations to find F2.
Q: What is the relationship between the magnitudes of F1 and F2?
A: We have determined that F1 = F2.
Q: What is the implication of F1 = F2?
A: The implication is that the two forces are equal in magnitude, and they act in the same direction.
Q: Can we conclude that the forces are equal in magnitude in all cases?
A: No, we cannot conclude that the forces are equal in magnitude in all cases. The problem statement only provides information about the net force in two specific cases, and we cannot make generalizations based on this limited information.
Q: What are some potential applications of this problem?
A: This problem has potential applications in physics, engineering, and other fields where forces and motion are involved. For example, it can be used to model the motion of objects under the influence of multiple forces.
Conclusion
In this article, we have answered some frequently asked questions related to the problem of two individual forces acting on a body of mass 1 kg. We hope that this Q&A article has provided a clear understanding of the problem and its solution.
Additional Resources
For more information on forces and motion, we recommend the following resources:
We hope that this article has been helpful in understanding the problem of two individual forces acting on a body. If you have any further questions or need additional clarification, please don't hesitate to ask.