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# Question 1a: 2015 AP Physics 1 free response

Free body diagram for two masses connected by string-pulley system.

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• At , why is the magnitude of the two tension forces the same? He says that it is because the tension is constant throughout the string due to the covalent bonds at the subatomic level. I find that hard to grasp. Could someone explain it a little bit further? • Is it possible for the string to have different tension forces on different parts? For example, on Block 2, could the tension force be m1g since that is the gravitational force of Block 1, which is pulling on the string? Likewise, could the tension force on Block 1 be m2g since that is the gravitational force of Block 2, which is pulling the string?

This would make the tension forces different for each Block and using this logic works for part b of the FRQ too. • At , why is the magnitude of the two tension forces the same? He says that it is because the tension is constant throughout the string due to the covalent bonds at the subatomic level. I find that hard to grasp. Could someone explain it a little bit further?
(1 vote) • At , why is the magnitude of the two tension forces the same? He says that it is because the tension is constant throughout the string due to the covalent bonds at the subatomic level. I find that hard to grasp. Could someone explain it a little bit further? • Tension is the same everywhere in a massless string. If it weren't the same everywhere, then you would have one bit of string that has more force on one side than it does on the other, and since the string is massless, that bit of string would have infinite acceleration.

Since there is no such thing as a real massless string, it doesn't really make any sense to try to refer to covalent bonds as an explanation for why the tension is the same throughout the string!
• I noticed that he never mentioned the force of air resistance. Are we just assuming that it is negligible? • Well actually it says in the question that m_2 = 2*m_1
Also... so the magnitude of tension is like arithmetic mean of the two masses?
Also... the tensions drawn in the answer are the same magnitude and direction, but actually they are opposite directions, because when you look at the string, since the pulleys are "negligible", you see that both point toward the center of the string, from different ends. So it makes sense to draw two tensions when you consider this as two systems, but you can also consider it one system, then there is no tension to take into account because it cancels out, and you have the overall acceleration equal m_1*g, or (m_2*g)/2, in the direction of the m_2 end of the string. But that doesn't answer the question since you have to draw two free body diagrams.
I'm just writing this so somebody could point out how wrong I am. • Why did you say that tension is the same? Wouldn't it be the tension is different because there are different directions of acceleration? (That's what you said when you drew it on the blocks instead of the space provided for your answer) • The position of a bicycle is described by the following function:

x(t)=a−b⋅t+c⋅t2

with a=31 m, b=4 ms, c=1.1 ms2.

v(t1)= ? ,v(t2)= ?
Please show how you solve them in steps and what equation you use.. thank you 