Help with Understanding Variables - Urgent!

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Understanding the differences between independent, dependent, controlled, and uncontrolled variables is crucial for grasping experimental design. The independent variable is the one you manipulate, such as time in the example of placing a hand on a hotplate, while the dependent variable, like pain, is what you measure in response. The relationship shows that as time increases, pain also increases, illustrating how the dependent variable relies on the independent one. Controlled variables are those you keep constant, such as the conditions under which the experiment is conducted, while uncontrolled variables can vary and affect the outcome. This explanation clarifies the roles of each type of variable in an experiment.
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in urgent need of help

i can't simply don't understand the differences between controlled uncontrolled independent and dependent variables if anyone can help its appreciatied :cry:
 
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You can think of independent as..well, the name of it. Think of a situation where...you put your hand on a hotplate. On a graph of time vs. pain, your time is your independent variable and pain is dependent. Why? Because the longer you keep your hand on the hotplate, the more it's going to hurt. Therefore, the amount of pain you feel is dependent on the time you leave it on there. If you leave your hand there for x time, you'll feel Y pain. If you leave it there for 10x time, you'll feel 100Y pain (or whatever). It doesn't really go the other way around. It's analogous for controlled and uncontrolled as well. You control the time you leave your hand there, and your pain is the uncontrolled.
 
thanks a million
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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