Pulley system (ideal pulley) Find the angle with vertical line

[thirteenheath]

Ideal pulley and strings, no friction.The pulley and the second string don't move.
I need to find the numerical value of theta, the acceleration of the two blocks and the tensions.Accelerations and tension must be given in terms of m and g.I guess
2T1=T2
T1=m2*a
m1*g-T1=m1*aTo find theta I need to know the angle between T2 and T2*cosθ.
Are these equations correct?What is missing?

 

[ehild]

Hi thirteenheath, welcome to PF.

T2, the tension in chord 2 is not parallel with the forces of tension (T1, one horizontal and one vertical), chord 1 exerts on the pulley. Add them as vectors to get the force on the pulley. As the pulley does not move, the resultant of the tensions must be zero.
You can eliminate T1 from the last two equation and get the acceleration of the blocks.

ehild

 

[thirteenheath]

Thanks ehild!

Oh I see...So if I understood we'll have

T1=T2*cosθ

T1=T2*sinθ

Then cosθ=sinθ and θ=45°.

Plus, through the last two equations in the previous post we find that

a=m1*g/(m1+m2).

Now I just need to replace the acceleration in any of the previous equations to find the values of T1 and T2.

Is that it?

Thanks again. =)

 

[ehild]

Thanks ehild!

Oh I see...So if I understood we'll have

T1=T2*cosθ

T1=T2*sinθ

Then cosθ=sinθ and θ=45°.

Plus, through the last two equations in the previous post we find that

a=m1*g/(m1+m2).


Now I just need to replace the acceleration in any of the previous equations to find the values of T1 and T2.

Is that it?

Thanks again. =)

Yes, it will be all right.

ehild

 

[Nickie]

Hello,

I would first like to clarify the situation described. From the given information, it seems that there are two blocks connected by a string running over an ideal pulley, and there is no friction in the system. The pulley and the second string are not moving. Additionally, the system is subject to the forces of gravity, represented by the acceleration due to gravity, g.

Now, to find the angle with the vertical line, we need to consider the forces acting on each block. The first block, with mass m1, is being pulled down by its weight, m1*g. This force is balanced by the tension in the string connected to it, T1. The second block, with mass m2, is being pulled up by the tension in the string connected to it, T2. Since the pulley is ideal, the tension in the string on either side of the pulley is equal, so we can say that T1 = T2.

To find the angle, we can use trigonometry and consider the right triangle formed by the two strings and the vertical line. The angle we are looking for is the angle between T2 and T2*cosθ. Therefore, we can say that T2*cosθ = m1*g. From this, we can find the value of cosθ, and then use inverse cosine to find the angle θ.

To find the accelerations of the two blocks, we can use Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F=ma). For the first block, we can say that the net force is equal to the tension in the string (T1), and the mass is m1. Therefore, we can say that T1 = m1*a1. Similarly, for the second block, we can say that T2 = m2*a2. Since we know that T1 = T2, we can equate these two equations to get m1*a1 = m2*a2. We also know that the acceleration due to gravity is acting on both blocks, so we can add this to the equation to get m1*a1 = m2*a2 + m1*g. From this, we can solve for the accelerations of both blocks, a1 and a2.

Finally, to find the tensions in the strings, we can use the equations we derived earlier for T1 and