Physics pulley question, why is my answer wrong?

[Howard]

There are two blocks connected by a rope, between them is a pulley. One block is on a flat surface, the other is hanging freely. The acceleration of the blocks is 5.1m/s^2. The mass of the smaller block (on the surface) is 10kg. The mass of the other block is 15kg.

When I solve for the tension in the rope, I get an answer of 51N (mass of smaller block multiplied by acceleration). Is this wrong?

 

[TuxDave]

^bump, my brain isn't working. Are you supposed to use the gravitational constant of 9.8m/s^2 in your calculations? Or is it not needed? Because what if there is some hidden frictional force that they're not telling you.

 

[Belethgaladwen]

are you given the mass or radius of the pulley?

 

[NeoPTLD]

Originally posted by: Howard
There are two blocks connected by a rope, between them is a pulley. One block is on a flat surface, the other is hanging freely. The acceleration of the blocks is 5.1m/s^2. The mass of the smaller block (on the surface) is 10kg. The mass of the other block is 15kg.

When I solve for the tension in the rope, I get an answer of 51N (mass of smaller block multiplied by acceleration). Is this wrong?

It doesn't make sense that 10kg mass can stay still on the surface when it's being pulled by 15kg mass.
At any rate, if the 15kg mass is hanging freely, the tension of rope is 76.5N between the pulley and free hanging mass.

 

[ZaneNBK]

I think you need to subtract the current accelleration from gravity to account for the pull on the rope. If they were both accellerating at the same rate then there would be little/no tension on the rope (but that would require little/no friction). I'm guessing it's (9.8 - 5.1) * 10Kg = 47N.

I took Physics 1 & 2 in HS but that was over 10 years ago so I'm mostly guessing.

 

[ZaneNBK]

Doh, got the masses backwards. Should be (9.8 - 5.1) * 15 = 70.5N

 

[TuxDave]

Originally posted by: ZaneNBK
I think you need to subtract the current accelleration from gravity to account for the pull on the rope. If they were both accellerating at the same rate then there would be little/no tension on the rope (but that would require little/no friction). I'm guessing it's (9.8 - 5.1) * 10Kg = 47N.

I took Physics 1 & 2 in HS but that was over 10 years ago so I'm mostly guessing.

Yeah, that's kinda what I was thinking, but take 10Kg and change it with 15Kg

Force due to gravity = 9.8*15Kg
Force actually being asserted onto 15Kg block = 5.1*15Kg
Leftover force being asserted through the rope = (9.8-5.1)*15kg = 70.5N

 

[Howard]

Originally posted by: TuxDave

Originally posted by: ZaneNBK
I think you need to subtract the current accelleration from gravity to account for the pull on the rope. If they were both accellerating at the same rate then there would be little/no tension on the rope (but that would require little/no friction). I'm guessing it's (9.8 - 5.1) * 10Kg = 47N.

I took Physics 1 & 2 in HS but that was over 10 years ago so I'm mostly guessing.

Yeah, that's kinda what I was thinking, but take 10Kg and change it with 15Kg

Force due to gravity = 9.8*15Kg
Force actually being asserted onto 15Kg block = 5.1*15Kg
Leftover force being asserted through the rope = (9.8-5.1)*15kg = 70.5N

I'm not getting this...

 

[GoodToGo]

Correct answer should be 70.5

T - 10a - 10g = 0
T+15a - 15g = 0

Either way you get T = 70.5

 

[Howard]

Originally posted by: GoodToGo
Correct answer should be 70.5

T - 10a - 10g = 0
T+15a - 15g = 0

Either way you get T = 70.5

Why?

 

[GoodToGo]

Originally posted by: Howard

Originally posted by: GoodToGo
Correct answer should be 70.5

T - 10a - 10g = 0
T+15a - 15g = 0

Either way you get T = 70.5

Why?

Its a force balance.

 

[SaturnX]

It's because you've been given an acceleration, therefore both masses are moving, and the smaller isn't going to move into the table, so it's obviously moving up, by moving upward, while the other is moving downward, both exhibit foreces of Tension and gravitional force.

It's irrelavent in which direction you set as positive, but if you look at each object independantly you see that for the 10kg block, it has the tension pulling upward (T), and mg downward, and an acceleration a. (in the direction of the tension), while the other block has gravitational force downward, and tension upward with an acceleration a (in the direction of the graviatational)

Thus you get the two equations

Solve for T, you get 70.5

--Mark

 

[Howard]

Originally posted by: Tharyn
It's because you've been given an acceleration, therefore both masses are moving, and the smaller isn't going to move into the table, so it's obviously moving up, by moving upward, while the other is moving downward, both exhibit foreces of Tension and gravitional force.

It's irrelavent in which direction you set as positive, but if you look at each object independantly you see that for the 10kg block, it has the tension pulling upward (T), and mg downward, and an acceleration a. (in the direction of the tension), while the other block has gravitational force downward, and tension upward with an acceleration a (in the direction of the graviatational)

Thus you get the two equations

Solve for T, you get 70.5

--Mark

The 10kg block is on a table?

OK, I understand that the block on the table undergoes only a force of tension, since it's on a flat surface, and that the block hanging undergoes a force of gravity exerted downward, and a force of tension "exerted" upward. But I still can't figure out the formulas to find the tension in the connecting rope...

 

[Triumph]

Originally posted by: Howard

Originally posted by: GoodToGo
Correct answer should be 70.5

T - 10a - 10g = 0
T+15a - 15g = 0

Either way you get T = 70.5

Why?

GoodToGo has it almost right. This is a common problem, and I saw people make this mistake all the time. The problem is you are setting T = mg. That is NOT correct. Have you draw your free body diagrams?

15kg block:
sumF=ma: T - 15(g) = 15(a)

10kg block:
sumF=ma: ....I'm not going to tell you what you missed here. Draw a free body diagram of the 10 kg block.

The tension is 225 N. My answer looks weird, but I can't find where I'm going wrong, so I'm going to stick with it.

 

[Howard]

Originally posted by: Triumph

Originally posted by: Howard

Originally posted by: GoodToGo
Correct answer should be 70.5

T - 10a - 10g = 0
T+15a - 15g = 0

Either way you get T = 70.5

Why?

GoodToGo has it almost right. This is a common problem, and I saw people make this mistake all the time. The problem is you are setting T = mg. That is NOT correct. Have you draw your free body diagrams?

15kg block:
sumF=ma: T - 15(g) = 15(a)

10kg block:
sumF=ma: ....I'm not going to tell you what you missed here. Draw a free body diagram of the 10 kg block.

The tension is 225 N. My answer looks weird, but I can't find where I'm going wrong, so I'm going to stick with it.

The answer in my textbook is 71N (I'm assuming it's 70.5N rounded, or something).

 

[Triumph]

Really? Damnit... T + 15a -15g = 0 gets you 71N. But that means that T and a () are in the same direction. And that means that the heavier block is accelerating upwards, which doesn't make sense. Well, I'm going to bed so I'm not looking at it anymore tonight!