a) What is the largestupward acceleration that the blocks can be given without e

Question

a)    What is the largestupward acceleration that the blocks can be given without eitherstring breaking?

(Take g = 9.8 m/s2.)

b)    If the upwardacceleration is slightly higher than this, which string breaks?

In Figure 4.7, two blocks are connected by a string, asshown, and the upper block is pulled upward by a differentstring. The masses of the upper and lower blocks are 300grams and 240 grams respectively. The string between theblocks will break if its tension exceeds 3.6 newtons, and thestring which pulls the combination upward will break if its tensionexceeds 7.8 newtons. a) What is the largestupward acceleration that the blocks can be given without eitherstring breaking? (Take g = 9.8 m/s2.) b) If the upwardacceleration is slightly higher than this, which string breaks?

Explanation / Answer

From top of the diagram to bottom, call the first part of thestring T1, and in between the blocks T2 m1 = 300g m2 = 240g
our two resulting equations are: (taking as a system, remember the internal forces will cancelwe can just take the two blocks to be one big block, and the forcesin the string between them cancel) T1 - (m1+m2)g = (m1+m2)a taking the bottom block by itself T2 - m2g = m2a the max values T1 = 7.8 newtons max T2 = 3.6 newtons , now we have : 7.8 N- (.3kg+.24kg)(9.8) = (.3kg+.24kg)a a = 4.64 m/s^2 -> goes any faster than this string 1will break. T2 - m2g = m2a 3.6n - (.24kg)(9.8) = .24a a = 5.2 m/s thus, fastest acceleration is 4.64 m/s^2, FOR EITHER string tobreak.... (since t1 will break at a faster acceleration thanthis..) and if it goes higher, first string will break

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