Tension Mass Problem: Same or Different Mass?

[madchemist]

Try this new one: If, while close to the surface of the Earth, I hold a block of mass (m) which is attached by a massless rope to a second block of the same mass, would the tension in the rope be any different when I let go of the first block? What about if the block's masses were different?

 

[Doc Al]

What do you think?

(Be sure to put questions like this in the Intro Physics forum, not Gen Physics.)

 

[madchemist]

I think that when the first block is released, the tension in the rope would be zero. I know these questions sound really stupid, but I'm being told that the tension would remain constant.

 

[Doc Al]

You are correct. Who told you it would remain constant?

 

[madchemist]

My physics professor at John Jay College, i.e., Professor I. Heard

 

[Doc Al]

Well, I'm sorry to hear that. To be charitable, I hope he just mispoke.

Ask him this: If the rope tension remains the same, that means the net force on the lower mass remains zero. If that were true, then it would just sit there in mid-air and not fall when you let go of the top mass.

 

[madchemist]

Alright, I'll try it. Thanks for your help- you've renewed my faith in Physicists.
Oh, and in case your curious about his reasoning...he thinks that IMMEDIATELY after you let go of the top block that both blocks are accelerating at the same rate (9.8 m/s2) AT ALL TIMES and that therefore the tension in the rope should be unchanged

 

[Doc Al]

Oh, and in case your curious about his reasoning...he thinks that IMMEDIATELY after you let go of the top block that both blocks are accelerating at the same rate (9.8 m/s2) AT ALL TIMES and that therefore the tension in the rope should be unchanged

Well... if he wants to talk about "immediately", I assume he's talking about the sub-microsecond time right after letting the mass go. It's true that it will take some (very small) time for the tension in the string to relax. But during that time the acceleration of the blocks cannot simply be 9.8 m/s^2.

Remind him that a falling mass will accelerate at 9.8 m/s^2 only if gravity is the sole force acting on it. Add the tension force and the acceleration must be different.