Question

s plus or minus 0.05cm = 2.5, 5.0, 10.0, 20.0, 30.0, 40.0
x plus or minus 0.05cm = 21.6, 20.6, 18.1, 13.9, 9.3, 5.0
1. if m is the mass of the meter rule, prove that -(100+m)x+l/m
2. plot a graph of s against x
3. what is the slope
4. from the graph find the value of s for which x=0
5. deduce the value of m from the graph

Answer 1

Let's address your questions one by one.

### 1. Proving the equation \(-\frac{(100+m)x + l}{m}\)

The relationship given seems to suggest a connection between variables \(s\), \(x\), and the mass \(m\). However, additional context or a relationship would be required to develop and prove this expression accurately. If we assume a linear relationship exists between \(s\) and \(x\), we typically start with a linear equation of the form:

\[
s = mx + b
\]

Where \(m\) is the slope and \(b\) is the y-intercept. The expression you've provided doesn't lend itself readily to verification without additional information. Assuming the physics context, \(l\) could represent a lever arm or distance, and \(100\) might refer to a constant force.

If you can provide more context or the specific origins of \(-\frac{(100+m)x + l}{m}\), I'd be happy to assist further.

### 2. Plot a graph of \(s\) against \(x\)

To plot a graph, we need to create a coordinate system where:

- The x-axis represents \(x\).
- The y-axis represents \(s\).

Based on your data, plot the pairs \((21.6, 2.5)\), \((20.6, 5.0)\), \((18.1, 10.0)\), \((13.9, 20.0)\), \((9.3, 30.0)\) and \((5.0, 40.0)\).

You would create a scatter plot with these points. Typically this is done using graphing software or graph paper.

### 3. What is the slope?

Once you have plotted the points on the graph:

- Use two points from the data you've plotted to find the slope (\(m\)).
- The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

You can select any two points. For example, using \((21.6, 2.5)\) and \((5.0, 40.0)\):

\[
m = \frac{40.0 - 2.5}{5.0 - 21.6} = \frac{37.5}{-16.6} \approx -2.26
\]

Please calculate it accurately based on the points you select.

### 4. From the graph, find the value of \(s\) for which \(x=0\)

To find the value of \(s\) when \(x=0\), look at the y-intercept of the line on your graph. The y-intercept is where the line crosses the y-axis (i.e., where \(x = 0\)).

If your line equation derived from the graph has the form \(s = mx + b\), then the \(y\)-intercept (where \(x=0\)) is simply \(b\).

### 5. Deduce the value of \(m\) from the graph

If the equation you derived is in the linear form from the graph (e.g., \(s = mx + b\)), you can identify \(m\) as the slope of the line you plotted earlier in step 3. Use the points you plotted to find \(m\) again, as discussed.

If \(s\) is linear with regard to \(x\) and you already computed the slope, that's your mass (\(m\)), given the context provided in the initial problem statement.

If you need further calculations or visual aids, please feel free to ask!