 # Newton's Second Law Lab Report

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Forces Investigation

Introduction & Aim
Newton’s Second Law states that the force of a given object “F,” is equal to its mass “m” multiplied by its acceleration “a”, hence the equation F=ma. This investigation aims to prove this law, by investigating the changes in acceleration of a cart being pulled by varying weights. What are the effects that varying forces have on the acceleration of an object?

Hypothesis
I predict that the greater the weight and therefore the force is that is pulling down on the cart, the greater the cart’s acceleration will be. By whatever amount the net force acting on the cart changes, I believe its acceleration will change proportionally. Because the relationship is linear, the results on the graph will be linear. This can be shown mathematically as: a ∝ F, or in words “a is proportional to F”. Therefore, a=kF, which can be rearranged to get F=(1/k)a. We know that F=ma where the mass is the cart plus the weights with friction considered, and we know that weight=mass x gravitational field strength. So, we use w-fric=ma instead of F=ma, where the force is substituted by the weight minus the friction. This can be rearranged to isolate a as such: a = (1/m)w - (1/m)fric and because w in this case represents F, it can be written as a= (1/m)F - (1/m)fric. This
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This supports my hypothesis, where I predicted this proportionality. From Newton’s Second Law F=ma, I derived an equation isolating a: a= (1/m)F - (1/m)fric. I solved the equation for the line of best fit, and used the y-intercept to figure out the friction, which was the only remaining unknown in the equation. Once the friction was known, I was then able to plug in measured values and verify my hypothesis. I proved with this equation, using examples from my data, that the force is in fact directly proportional to