Of two blocks (of masses m1 and m2) tied together with a massless rope that passes over a fixed, perfect (massless and frictionless) pulley. In this problem you'll investigate some special cases where physical variables describing the Atwood machine take on limiting values. Often, examining special cases will simplify a problem, so that the solution may be found from inspection or from the results of a problem you've already seen.
For all parts of this problem, take upward to be the positive direction and take the gravitational constant, g, to be positive.
Part A
Consider the case where m1 and m2 are both nonzero, and m2>m1. Let T1 be the magnitude of the tension in the rope connected to the block of mass m1, and let T2 be the magnitude of the tension in the rope connected to the block of mass m2. Which of the following statements is true?
Consider the case where and are both nonzero, and . Let be the magnitude of the tension in the rope connected to the block of mass , and let be the magnitude of the tension in the rope connected to the block of mass . Which of the following statements is true?
T1 is always equal to T2.
T2 is greater than T1 by an amount independent of velocity.
T2 is greater than T1 but the difference decreases as the blocks increase in velocity.
There is not enough information to determine the relationship between T1 and T2.
Part B
Now, consider the special case where the block of mass m1 is not present. Find the magnitude, T, of the tension in the rope. Try to do this without equations; instead, think about the physical consequences.
T =
Part C
For the same special case (the block of mass m1 not present), what is the acceleration of the block of mass m2?
Express your answer in terms of g, and remember that an upward acceleration should be positive.
a2 =
Part D
Next, consider the special case where only the block of mass m1 is present. Find the magnitude, T, of the tension in the rope.
T =
Part E
For the same special case (the block of mass m2 not present) what is the acceleration of the end of the rope where the block of mass m2would have been attached?
Express your answer in terms of g, and remember that an upward acceleration should be positive.
a2 =
Part F
Next, consider the special case m1=m2=m. What is the magnitude of the tension in the rope connecting the two blocks?
Use the variable m in your answer instead of m1 or m2.
T =
Part G
For the same special case (m1=m2=m), what is the acceleration of the block of mass m2?
a2 =
Part H
Finally, suppose m1??, while m2 remains finite. What value does the the magnitude of the tension approach?
T =