Find the weight of a sphere connected to a pulley and to wall

[MaiteB]

Homework Statement

The system of 2 spheres is in equilibrium. Figure:

. If the weight of the second sphere P2=20N, ABC=60 degrees and BAC=30 degrees, find the weight of the first P1 and the force that is applied on the drum of the pulley.

Homework Equations

P1=m*a

The Attempt at a Solution

Everything is in equilibrium (no acceleration). I think I should solve Newtons 2nd law for P2 to tell me the tension, but I have no acceleration for P2. I don't know how to solve it.

 

[Orodruin]

Everything is in equilibrium (no acceleration). I think I should solve Newtons 2nd law for P2 to tell me the tension, but I have no acceleration for P2. I don't know how to solve it.

You have basically answered your own question. What is the numerical value of the acceleration if you have no acceleration?

 

[MaiteB]

You have basically answered your own question. What is the numerical value of the acceleration if you have no acceleration?

I think it's 0, but it has no sense.

 

[Orodruin]

I think it's 0, but it has no sense.

Why not?

 

[MaiteB]

Why not?

And the force would be 0? This is the answer? Can you give me a clue?

 

[Orodruin]

And the force would be 0? This is the answer? Can you give me a clue?

Which force would be zero?

 

[MaiteB]

Which force would be zero?

The tension

 

[Orodruin]

The tension

Is the tension the only force acting on the object?

 

[MaiteB]

Is the tension the only force acting on the object?

No, it's also the gravity

 

[Orodruin]

So what is the acceleration of the object if it is acted upon by a gravitational force mg and a tension force 0?

 

[MaiteB]

So what is the acceleration of the object if it is acted upon by a gravitational force mg and a tension force 0?

g

 

[Orodruin]

Exactly, so tension cannot be zero for zero acceleration. What tension do you need for zero acceleration?

 

[MaiteB]

Exactly, so tension cannot be zero for zero acceleration. What tension do you need for zero acceleration?

The tension should be 20 N?

 

[Orodruin]

Yes, equilibrium means that the resultant force (obtained by adding all forces acting on the object) is zero.

 

[MaiteB]

Yes, equilibrium means that the resultant force (obtained by adding all forces acting on the object) is zero.

The numerical answer is in my book. It is 17,3 N (it should be about the force that is applied on the drum). So in order to find it I used the formula P1 according to the drum direction is sin30*20=10 and the P force directed towards the wall is sin60*20=17.3. But in oreder to get the right answer shouldn't it be the vice versa?

 

[MaiteB]

The numerical answer is in my book. It is 17,3 N (it should be about the force that is applied on the drum). So in order to find it I used the formula P1 in the vector to the drum direction is sin30*20=10 and the P force directed towards the wall is sin60*20=17.3. But in oreder to get the right answer shouldn't it be the vice versa?

 

[MaiteB]

I have this other idea: I found the force applied on the drum with the formula cos 30*20=17.3 N. Then I calucated the P1 knowing that the vector in the direction of the drum is 17.3 N, I found the P1 which is 17,3*2=34.4 (CB is in front of 30 grades angle.)

 

[MaiteB]

I have this other idea: I found the force applied on the drum with the formula cos 30*20=17.3 N. Then I calucated the P1 knowing that the vector in the direction of the drum is 17.3 N, I found the P1 which is 17,3*2=34.4 (CB is in front of 30 grades angle.)

Yes, equilibrium means that the resultant force (obtained by adding all forces acting on the object) is zero.

Can you see my last answer and let me know if I got it right?

 

[haruspex]

I have this other idea: I found the force applied on the drum with the formula cos 30*20=17.3 N. Then I calucated the P1 knowing that the vector in the direction of the drum is 17.3 N, I found the P1 which is 17,3*2=34.4 (CB is in front of 30 grades angle.)

The "force on the drum" is a result of both the tension in the vertical section and the (same) tension in the BC sectIon. You have only calculated the vertical component of the tension in BC.
The string AC is separate. It may have a different tension from that in BC. You have to figure that out by considering horizontal equilibrium.