Question

(Figure 1) shows an acceleration-versus-force graph for three objects pulled by rubber bands. The mass of object 2 is 0.30 kg . The graph reads: object 1 a=5 and force of 2 rubber bands. Object 2 a= 5 and force of 5 rubber bands. Object 3 a=2.5 with force of 6 rubber bands. What is the mass of objects 1 and 3?

Answer 1

The Overall equation for F:

F = m a (1)

m = F/a (2)

The acceleration versus Force graph, (even though it's not available), we can actually calculate mass of object 1 and 3. So, from the first equation, we calculate acceleration, and with that data we can calculate the rest:

5 N = 0.3 kg x 5a -----> a = 1/0.3 = 3.33 m/s² = a = a1

Now, I manage to find the graph on another site, so, with the value of aa, we can now calculate the value of m of object 3 and 1 so, applying equation 2:

m1 = 2 / 5x3.33

m1 = 0.12 kg

m3 = 6 / 2.5x3.33

m3 = 0.72 kg

Thios would be one way to solve it, now that we don't actually have the graph here. However, looking in different sources, I found the graph for this problem, and the other way to do this is calculating the slope of all lines. The acceleration is calculated the same way as before (because it's the most linear and have an a:F relation of 1:1), so a = a1 and all the graph is expressed as a1. so it's neccesary to determine the slope of object 1 and 3:

a = F (1/m) or simply: y = 1/x

If you do this, you'll get the same (or very similar) values that I obtained with the innitial data. If you need more explanation, feel free to message me in a comment. Regards.