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How can we change a system but keep the acceleration constant?
Using the simulation:
Start with a system of:
Cart = 0.25 km
Force (0.30kg*9.8N/kg) = 2.94 N
Suppose we were to change the system in one of two ways:
Add equal amounts of mass to both the mass of the cart and the hanging mass (Force). For example add 0.05 kg to both cart and hanging mass. The changes in acceleration will be subtle but important. - OR-
Add proportional amounts to both the mass of the cart and the hanging mass (Force). For example, make the new mass of the cart 1.2x larger and the hanging mass 1.2x larger as well.
N2L Simulation Setup:
N2L Simulation Setup:
While the differences in the acceleration are subtle when adding equal amounts to both the cart and hanging mass, these differences are important both physically and mathematically.
If the initial values for the force (F) is 3N and mass (m) is 4 kg, the equation would be:
If equal values are added to each, as in #1, the new equation would be:
However, if both values are increased proportionately, as in #2, the new equation is:
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