TBR Physics, Ch.2, Passage IV, Question 25

[cafeverona]

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The answer they gave was qualitative and based on the fact that pulling a block with an upward directed tension decreases the normal force, and thus decreases the friction and horizontal tension.

However, when I try to sum the forces, I don't understand why the horizontal tension is smaller in case 2 in comparison to case 3. I keep getting that they are the same. Can someone explain this to me quantitatively?

 

[Cawolf]

Are you giving them the correct signs?

The angles are the same but the vectors point in different directions.

We know in both cases that a = 0 due to the statement of constant velocity.

I would work it all out and post it, but pretty busy and it would take a bit.

You know the force of friction = (mu)(normal force)

When the tension force is pointed up, (Ft)(sin 30) is subtracted from the normal force - making the frictional force less, and the tension less.

When the tension force is pointed down, (Ft)(sin 30) is ADDED to the normal force - making the frictional force greater, and the tension greater.

 

[cafeverona]

Oh yeah you're completely right. Gotta keep track of those signs haha. I think I just took into account the fact that Ftx was positive in each case without realizing that Fty was opposite and would change the horizontal tension. Thank you!

 

[Cawolf]

Yup, no problem.

I will also note that on this problem, you should not be summing forces. It will take you forever.

This problem is an example of something that is intuitive if you've ever tried to move something up a hill. Pulling is always easier than pushing, because when you push into the ground you increase the normal force and frictional force - making the trip a lot harder!

 

[cafeverona]

Yeah--I understood the qualitative answer, but I tend to be uncertain unless I have some math to back it up. 🙂