EK 1001 physics #241

[generator]

---

Members do not see this ad.

So a 50 kg woman dangles a 50 kg mass from the end of a rope. If she stands on a frictionless surface and hangs the mass over a cliff with a pulley (all of this is shown in the attachment) ... what is the tension in the rope?

A. 0 N
B. 250 N
C. 500 N
D. 1000 N

The answer is B.

The explanation in the back tells me that since the mass and the woman are the same weight, the acceleration is half of g... and this means the tension is half mg. I don't understand why... please help me?



Thanks

 

[exquisitemelody]

I don't really get that explanation of acceleration, but...

Draw FBD for both objects. For the woman, the only force on her is tension, so Fnet=T which is ma=T. For the block, if we call downward positive, Fnet=mg-T or ma=mg-T. Because the mass and acceleration of the objects are the same (they're connected, so same acceleration, and the problem told you they were the same mass), you can substitute ma=T into ma=mg-T. This gives you T=mg-T. Solve for T and you get 250.

For some reason, this doesn't work if you call upward positive...maybe it's because you have to follow the direction of the T you chose for the woman and use the direction of the rope to decide what to call positive? I dunno...can someone enlighten me?

 

[Arctangent]

I don't really get that explanation of acceleration, but...

Draw FBD for both objects. For the woman, the only force on her is tension, so Fnet=T which is ma=T. For the block, if we call downward positive, Fnet=mg-T or ma=mg-T. Because the mass and acceleration of the objects are the same (they're connected, so same acceleration, and the problem told you they were the same mass), you can substitute ma=T into ma=mg-T. This gives you T=mg-T. Solve for T and you get 250.

For some reason, this doesn't work if you call upward positive...maybe it's because you have to follow the direction of the T you chose for the woman and use the direction of the rope to decide what to call positive? I dunno...can someone enlighten me?

I think it still works if up is positive. For the woman:
Fnet = ma = -T

For the block:
Fnet = ma = T + mg (designating g as -10m/s^2)

So following the substitution:
T + mg = -T
2T = -mg
T = -mg/2 (Since g is negative, it cancels and you get a positive tension with magnitude mg/2

 

[exquisitemelody]

How do you know to designate the woman's tension as negative?

 

[Arctangent]

How do you know to designate the woman's tension as negative?

Based on the attachment, if I designated down as negative, then following the pulley past its turn, then left would also be negative, which should be the direction the tension is pulling the woman.