Sketch two forces vs.extension graphs,one for a stiff spring the other for a much weaker spring.
To sketch two forces vs. extension graphs for a stiff spring and a weaker spring, we need to understand the relationship between force and extension in each case. The force vs. extension graph is based on Hooke's Law, which states that the force exerted by a spring is directly proportional to its extension.
Let's start with the stiff spring. A stiff spring has a higher spring constant (k), which indicates that it is harder to stretch or compress compared to a weaker spring. As a result, a greater force is required to produce the same amount of extension.
To sketch the graph for a stiff spring:
1. Take a horizontal axis and label it "Extension (x)".
2. Take a vertical axis and label it "Force (F)".
3. Initially, at zero extension, there would be no force applied. This point will be the origin of the graph.
4. As extension increases, the force exerted by the stiff spring also increases rapidly, following a linear relationship. Therefore, the graph will show a steep upward slope as extension increases.
Now let's consider a weaker spring, which has a lower spring constant (k). This means it is easier to stretch or compress compared to a stiff spring. Consequently, a smaller force is needed to achieve the same extension.
To sketch the graph for a weaker spring:
1. Use the same horizontal and vertical axes as before.
2. Initially, there is no force applied at zero extension. This point will be the origin, like in the previous graph.
3. Unlike the stiff spring, a weaker spring requires less force to produce the same extension. Therefore, the graph will have a gentler upward slope as extension increases.
Remember, both graphs should start from the origin (zero extension and zero force) since no force is applied at the beginning. The difference lies in the steepness of the slope. The graph for a stiff spring will have a steeper slope, indicating a stronger force-to-extension relationship, while the graph for a weaker spring will have a gentler slope, indicating a weaker force-to-extension relationship.