Question

12 mark for review a uniform rope with nonnegligible mass is attached to a block in two different situations, as shown in the figures. in situation 1, the block is suspended from the ceiling and remains motionless. in situation 2, the rope can be modeled as completely horizontal. in which situation, if either, does the magnitude of the tension at point a equal the magnitude of the tension at point b? a situation 1 only b situation 2 only c both situations d neither situation

Explanation:

Step1: Analyze Situation 1

In Situation 1, the block is motion - less. Let the mass of the rope be $m$ and the mass of the block be $M$. Consider a section of the rope between point $A$ and the block. The tension at point $A$, $T_A$ supports the weight of the block $Mg$ and the weight of the rope below point $A$. Consider a section of the rope between point $B$ and the block. The tension at point $B$, $T_B$ supports the weight of the block $Mg$ and the weight of the rope between $A$ and $B$ and the weight of the rope below $A$. So $T_B>T_A$.

Step2: Analyze Situation 2

In Situation 2, the rope is accelerating to the right. Let the mass per unit length of the rope be $\lambda$. Consider a section of the rope between point $A$ and the end attached to the block. Let the length of the rope between $A$ and the block be $l_A$ and the length between $B$ and the block be $l_B$ with $l_B > l_A$. According to Newton's second law $F = ma$. The tension at point $A$, $T_A$ causes the acceleration of the rope of length $l_A$ and the block. The tension at point $B$, $T_B$ causes the acceleration of the rope of length $l_B$ and the block. Since $l_B>l_A$, $T_B>T_A$.

Answer:

D. Neither situation