three spheres

https://isaacphysics.org/questions/three_spheres?stage=a_level

kind of got confused halfway, this is my working so far. upon putting in T = 1.85, isaac physics says

You may have not resolved some of your forces correctly, particularly when trying to work out the component of the force on the lower balls that acts in the direction of one of the tension forces.
It can be hard to visualise things in 3D, so make sure you are careful when drawing your diagrams.

can someone see where i went wrong in calculating R

Agree with your value of R, though I'd work to a higher number of sig.fig. than 3, if you want the answer to 3 sig.fig. (R=3.204 N to 4 sig.fig.). In fact I'd leave everything in terms of variables and exact values until the final working.


Then considering horizontal forces on a single sphere, $R\cos\theta$ is the horizontal component of the reaction between the top and one of the lower spheres, where $\theta$ is the angle between the reaction and the horizontal. Think you've got that.

But this does not equal $2T$. since the tensions are at an angle to the horizontal component of the reaction; and this is where you have your error.

i think I’ve got it, am I right in saying Rcos(theta) = 2Tcos30

i think I’ve got it, am I right in saying Rcos(theta) = 2Tcos30