To facilitate a whole-class conversation about the relationship between the force of gravity on an object and its mass, have each lab group record their graph and resulting equation on a large whiteboard. Have the class circle up so that everyone can clearly see the graphs and equations on each whiteboard. Remember that your goal is to help facilitate a conversation that allows your students to make connections and draw conclusions from the graphs and equations.
Start by asking students to compare the graphs and equations on the whiteboards and identify any similarities or differences they see. For this lab, students will have similar graph shapes, slope values, and y-intercept values. Once the similarities and differences are identified, the rest of the conclusion discussion should focus on what the shape of the graph suggests about the relationship between variables, the meaning of the slope, and the significance of the y-intercept.
After the students identify the shape of all the graphs is linear, ask them what this indicates about the relationship between the force of gravity on an object and its mass. The students should be able to identify that the linear shape suggests that the force of gravity will increase in size by the same amount when the mass is increased in equal increments. When looking at the slope values it should be clear that the force of gravity in all cases seems to increase by approximately 10N for each 1kg of mass. This is the meaning of the slope you want students to recognize: that there is approximately 10N of gravitational pull on every kilogram of an object’s mass.
When the students look at the values of the y-intercepts they will have small positive or negative values. The question becomes whether these values are significant or insignificant. To help students judge the significance of a y-intercept, it is not enough to just look at the value. The value of the y-intercept must be compared with the range of values collected on the y-axis, in this case, the gravitational force values. The threshold is somewhat arbitrary, but I tell my students that the y-intercept is insignificant if it is less than 5% of the maximum y-value. If this is the case, the y-intercept of the linear fit could reasonably be explained as a result of measurement errors. The y-intercept can also be considered insignificant if it can be reasoned away. Have the students think about what they would expect the y-intercept to be in this experiment. Here is a way you could ask the question: “As the mass of the hanging object gets smaller and smaller, approaching zero, what would you expect the value of the gravitational force to approach? Students will be able to identify that as the mass of the object approaches zero, they would expect the force of gravity on that object to also approach zero. If the y-intercept can be reasoned away, it can be left out of the algebraic equation.
After the students reach a consensus about the meaning of the slope and the significance of the y-intercept, you can introduce the concept of “gravitational field strength” and write the general equation on the board. The general equation shows the relationship between the force of gravity on an object and the object’s mass. Tell students that the formal name given to the slope in this experiment is the Earth’s “gravitational field strength”, the size of the gravitational force experienced by each kilogram of an object’s mass near the Earth’s surface. The accepted gravitational field strength for the Earth is 9.8 newtons for each kilogram. The symbol used to represent gravitational field strength is a lower case “g”, so the general equation can be written as the force of gravity exerted on an object is equal to the gravitational field strength of the planet multiplied by the object’s mass. The equation is usually written as Fg = mg.
After this lab experience, your students should have a much clearer understanding of the meaning of both mass and weight and a quantitative way to think about how the two are related.