Issac physics, climbing up a corner, static challenge 3

https://isaacphysics.org/questions/corner_climbing?board=be0dac43-6ba3-44d5-9a77-091234eef766&stage=a_level

I think the theta should be 30 degrees so mu=1 and the friction equals to normal reaction, I calculated the pushing force using from adding the friction and normal reaction (vectors) together and got this. but it's wrong

my method will be uploaded in the discussion

The total force applied on each wall will comprise of the normal reaction force and the frictional force where the normal reaction force is perpendicular to the wall and the frictional force is in the wall plane so has a x (horizontal) and a y (vertical) component and z is normal to the wall. Once you have those two forces, you can use pythagoras to combine.

For the frictional force in the wall plane, consider balancing forces on one wall
* the frictional force in the x direction must balance N from the other wall
* the frictional force in the y direction must balance half the weight
* the normal reaction force must satisfy Fr <= mu N, where Fr is the total frictional force given by combining the two components. You want the minimum force necessary.

That should be enough to get Fr (wall plane) and therefore N (perpenicular to the wall) and combine using pythagoras.

Note in the OP you say that mu should be 1. Obviously the solution is a function of mu, and mu=1 is nothing special. It could be greater be than 1, which would simply mean that the friction force is greater than the normal force, Climbing shoes have rubber soles precisely for this reason. Also, with hindsight, Id guess you could use a trig argument to get the frictional force in the wall plane. Initialy, a component approach seemed the most systematic, but it may be worth fleshing out the trig one.

thank you so much! I think I used the same method (a bit proud)? but I'm a bit confused about the fleshing out of the trig. cuz I always have a cos(theta) in my denominator....and I substituted theta=30 in the OP

okay, I'll do that

Out of interest, is your theta the same theta as per hint 2? Its not clear in their diagram, but Im presuming their theta was in the wall plane, which Im not sure yours was?

my theta is the angle between the friction and the wall, and think so does the theta in their diagrams. I haven't learnt three dimension coordination yet... are you making every forces into coordinates and calculate the distance? (thanks for baring the stupid question)

The total force applied on each wall will comprise of the normal reaction force and the frictional force where the normal reaction force is perpendicular to the wall and the frictional force is in the wall plane so has a x (horizontal) and a y (vertical) component and z is normal to the wall. Once you have those two forces, you can use pythagoras to combine.

For the frictional force in the wall plane, consider balancing forces on one wall
* the frictional force in the x direction must balance N from the other wall
* the frictional force in the y direction must balance half the weight
* the normal reaction force must satisfy Fr <= mu N, where Fr is the total frictional force given by combining the two components. You want the minimum force necessary.

That should be enough to get Fr (wall plane) and therefore N (perpenicular to the wall) and combine using pythagoras.

Note in the OP you say that mu should be 1. Obviously the solution is a function of mu, and mu=1 is nothing special. It could be greater be than 1, which would simply mean that the friction force is greater than the normal force, Climbing shoes have rubber soles precisely for this reason. Also, with hindsight, Id guess you could use a trig argument to get the frictional force in the wall plane. Initialy, a component approach seemed the most systematic, but it may be worth fleshing out the trig one.

ohhh I got it!!! yayya! thank you so much!!! I didn't get enough sleep previously but I got enough sleep today hahaha~ thank you so much!!!!

actually I think mu cannot be equal to one but more than 1, or the denominator will be 0?
it has to be larger than 1 to balance the weight and the normal reaction?

Exactly. Its only with a frictional coefficient > 1 that tthey can successfully climb a corner like this.

ohhh I got it!!! yayya! thank you so much!!! I didn't get enough sleep previously but I got enough sleep today hahaha~ thank you so much!!!!