Below is a diagram of two blocks connected by a string. A second
string attached to the red block is pulled to the right so that it
has a tension of 10 N. Which of the following is true of the string
between the red and blue blocks? Explain your choice.
a. The tension is less than 10 N.
b. The tension is equal to 10 N.
c. The tension is more than 10 N.
d. Can't be answered without knowing the masses of the
blocks.
The correct answer is a. Consider both
blocks as a single system. This system is accelerated by the 10 N
force exerted by the string on the right. Thus the acceleration of
the system (and each block in the system) is given by that 10 N force
divided by the combined masses of the two blocks. The blue block is
accelerated by the middle string alone, so the magnitude of the
tension in the middle string must be the product of the mass of the
blue block and the acceleration of the blue block (T =
mblue * 10 N / (mblue + mred) ). The
magnitude of this tension is therefore, less than 10 N.
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