Question

This problem concerns the concept of tension in a rope.Consider a rope subjected to a pulling force on its two ends asshown.(Intro 1figure)The rope isstationary. An arbitrary point P divides the rope into a left-handsegment L and a right-hand segment R. $MFS_3l_10_a.jpg$ Assume that segment R exerts a force ofmagnitude on segmentL. What is the magnitude $F_RL$ of the force exerted onsegment R by segment L?Give your answer in terms ofand other constants such as.Now imagine two points, Q and P, that dividethe rope into segments L, M ,and R.(Part Cfigure)The rope remains stationary.Assume that segmentL exerts a force of magnitude $F_LM$ on segment M. What is the magnitude $F_RM$ of the forceexerted by segment R on segment M?Give your answer in terms of $F_LM$ and constants such as.Now consider a rope that, unlike thoseusually studied in mechanics problems, actually has a significantmass .The tension at the right end of this rope is $T_2$ and that at the left end is $T_1$ .(Part D figure)Therope has an acceleration $a_rope$ to the right.

Complete the following equation for the acceleration of thesection of the rope of mass ,taking the positive direction to be to the right.

Give your answer in terms of $T_1$ , $T_2$ , and constants such as .

Answer 1

F_RL=T since the ropes are stationary and the right halfof the rope exerts T on the left side

F_RM=F_LM , also because the rope isstationary, which means these forces are equal, but opposite

Answer 2

Part D: Now consider a rope that, unlike thoseusually studied in mechanics problems, actually has a significantmass .The tension at the right end of this rope is $T_2$ and that at the left end is $T_1$ .(Part D figure)The rope has an acceleration $a_rope$ to the right. Complete the equation: F_Rope = ma_rope = ___________.  Answer in terms of T₁, T₂ and constants like g.

A: T₂- T₁.

Answer 3

Part E

Which of the following phrases, if they appear in a problem, allow you to assume that T2=T1in a horizontally oriented rope.

1. The rope is massless.
2. The rope is moving at constant speed.
3. The rope is stretched with negligible sag.

 

 

Which of the following phrases, if they appear in a problem, allow you to assume that T_2 = T_1 in a horizontally oriented rope?

1. The rope is massless.
2. The rope is moving at constant speed.
3. The rope is stretched with negligible sag.

	A only
	B only
	C only
	A or B
	A or C
	B or C
	A or B or C

Answer A or B. C only shows T1 = T2 > mg.

Answer 4

More on partE below:

 

Having either negligible mass or being in uniform motion (constant velocity) both cause T1=T2 . This can be seen using Newton's 2nd law: ΣF⃗=ma⃗ . The net force F⃗ is given by T2−T1 . If m≈0 or if a⃗=0 then the net force will be zero, implying that T1=T2 .