Rotational Dynamics: Confused about the tension in this string pulling a mass up an incline

• B
• Sep
Sep
TL;DR Summary
I am confused why the solutions say that Mgsin(theta) is greater than tension. Isn't tension greater because the block is going up the incline? Or is it that in cases where the block is decelerating but still going up, the force of gravity will be greater?
Question

giving a=Mgr2sinθI+Mr2​

I am confused why the solutions say that Mgsin(theta) is greater than tension. Isn't tension greater because the block is going up the incline? Or is it that in cases where the block is decelerating but still going up, the force of gravity will be greater?

Sep said:
Isn't tension greater because the block is going up the incline?
The block has positive velocity upwards, but that has nothing to do with the tension. Consider that if we cut the string the block would still keep coasting up the ramp for a while, until gravity brought it to a stop and started it back down.

Sep
Nugatory said:
The block has positive velocity upwards, but that has nothing to do with the tension. Consider that if we cut the string the block would still keep coasting up the ramp for a while, until gravity brought it to a stop and started it back down.
Oh, I understand now. The initial velocity. Thank you so much!

Nugatory and berkeman

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