A force and its equivalent can be interchanged in terms of their effect on an object, following the parallelogram rule. Since a force has two main effects—changing the motion state of an object (motion effect) and causing it to deform (deformation effect)—the question arises: under what conditions and for which effect can these forces be considered equivalent?
Physics tells us that:
1. A system of forces acting on a particle can always be replaced by a single equivalent force.
2. For a rigid body, a force system is usually not equivalent to a single force. Instead, it may require both a force and a couple (moment). However, if the forces act at the same point (a concurrent force system), they can still be replaced by one resultant force.
3. When dealing with non-rigid bodies, where deformation is significant, the force system cannot be simplified into a single force.
In summary, only systems acting on particles or concurrent forces on rigid bodies can be replaced by a single equivalent force. If deformation is involved, regardless of whether the forces are concurrent or not, they cannot be simplified to a single force. In such cases, the parallelogram rule loses its physical meaning. However, when the focus is solely on the motion effect, even if deformation occurs, the forces can still be replaced by an equivalent force.
For example, using the parallelogram rule to find the resultant of F1 and F2 in Figure 1 and then using this resultant to describe the deformation of a spring is physically meaningless. It’s illogical to claim that a person experiencing two equal and opposite forces feels no force at all, especially when considering the actual physical deformation. Similarly, two equal and opposite forces applied at different points on a circular plate will not have the same effect as no force at all.
Given that equivalence of forces doesn’t apply to deformation, why do physics textbooks use experiments like the rubber band setup to demonstrate the parallelogram law? Take the classic experiment where a small ball is fixed at a node. When pulled to the same position twice, the rubber bands deform equally. According to Hooke's Law, the restoring force from the rubber bands is the same each time. The ball remains stationary, so the tension balances the restoring force. This method effectively transforms a dynamic situation into a static one, making it easier to measure. The key idea here is that the equivalence of forces is reflected through the deformation, which allows us to verify the parallelogram rule indirectly.
In conclusion, understanding the basic principles of forces and springs helps form a coherent conceptual framework. Only with this foundation can we accurately interpret and answer related questions.
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