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

In summary, the problem involves finding the weight of the first sphere P1 and the force applied on the drum of the pulley, given that the system of two spheres is in equilibrium and the weight of the second sphere P2 is 20N, ABC is 60 degrees and BAC is 30 degrees. The solution involves solving for Newton's 2nd law and considering horizontal equilibrium to find the tension in the string AC. The final answer can be calculated by using the formula P1 = sin30 * 20 = 10 and then finding the tension in BC by using cos30 * 20 = 17.3 N.
  • #1
MaiteB
44
0

Homework Statement



The system of 2 spheres is in equilibrium. Figure:
uPHmi.png
. 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.
 
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  • #2
MaiteB said:
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?
 
  • #3
Orodruin said:
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.
 
  • #4
MaiteB said:
I think it's 0, but it has no sense.
Why not?
 
  • #5
Orodruin said:
Why not?
And the force would be 0? This is the answer? Can you give me a clue?
 
  • #6
MaiteB said:
And the force would be 0? This is the answer? Can you give me a clue?
Which force would be zero?
 
  • #7
Orodruin said:
Which force would be zero?
The tension
 
  • #8
MaiteB said:
The tension
Is the tension the only force acting on the object?
 
  • #9
Orodruin said:
Is the tension the only force acting on the object?
No, it's also the gravity
 
  • #10
So what is the acceleration of the object if it is acted upon by a gravitational force mg and a tension force 0?
 
  • #11
Orodruin said:
So what is the acceleration of the object if it is acted upon by a gravitational force mg and a tension force 0?
g
 
  • #12
Exactly, so tension cannot be zero for zero acceleration. What tension do you need for zero acceleration?
 
  • #13
Orodruin said:
Exactly, so tension cannot be zero for zero acceleration. What tension do you need for zero acceleration?
The tension should be 20 N?
 
  • #14
Yes, equilibrium means that the resultant force (obtained by adding all forces acting on the object) is zero.
 
  • #15
Orodruin said:
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?
 
  • #16
MaiteB said:
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?
 
  • #17
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 teh 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.)
 
  • #18
MaiteB said:
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 teh 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.)
Orodruin said:
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?
 
  • #19
MaiteB said:
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 teh 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.
 

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

1. How do you find the weight of a sphere connected to a pulley and a wall?

The weight of a sphere connected to a pulley and a wall can be found by using the formula W = m x g, where W is the weight, m is the mass of the sphere, and g is the acceleration due to gravity.

2. What is the purpose of using a pulley in this scenario?

The purpose of using a pulley in this scenario is to make it easier to lift or move the sphere by distributing the weight evenly and reducing the amount of force needed to lift the sphere.

3. How does the weight of the sphere affect the tension on the pulley?

The weight of the sphere affects the tension on the pulley by increasing the tension on the rope or cable connected to the pulley. This is due to the fact that the weight of the sphere is being supported by the tension in the rope or cable.

4. Can the weight of the sphere be determined if the pulley is not in equilibrium?

Yes, the weight of the sphere can still be determined even if the pulley is not in equilibrium. This can be done by using the equation W = T x r, where W is the weight, T is the tension in the rope or cable, and r is the radius of the pulley.

5. Are there any factors that can affect the accuracy of the weight measurement in this scenario?

Yes, there are a few factors that can affect the accuracy of the weight measurement in this scenario. These include the friction in the pulley system, the accuracy of the measurement of the tension in the rope or cable, and any external forces acting on the sphere.

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