Find the minimum and maximum of a ratio for equilibrium

AI Thread Summary
The discussion focuses on determining the minimum and maximum ratio of l/d for a rod in equilibrium, considering static friction at points A and B. The user has calculated the forces acting on the rod just before sliding occurs but is uncertain about the next steps. They need to express the solution as an inequality involving the coefficient of static friction (μ_s) and the angle (θ). There is a suggestion to incorporate four forces and three torques into the calculations. The conversation emphasizes the importance of these calculations to establish the required ratio for equilibrium.
Aleph_null
Messages
2
Reaction score
0

Homework Statement



3nC4k33.png


Consider the rod as shown in the figure. The coefficient of static friction at A and B is \mu_s. I'm trying to find how big and how small the ratio l/d can be for the rod to still be in equilibrium. I have calculated how big all forces are acting upon the rod in the case just before sliding happens, but I'm not sure how to proceed.

Homework Equations



Just before sliding happens the friction force F is F = \mu_s * F_n, where F_n is the normal force.

The Attempt at a Solution

 
Physics news on Phys.org
They want the solution as an inequality in terms of \mu_s and theta, .i.e they want a LS and RS as LS < l/d < RS .
 
Aleph_null said:
I have calculated how big all forces are acting upon the rod in the case just before sliding happens, but I'm not sure how to proceed.

Have you? Could you show us that calculation? Did it involve 4 forces and 3 torques all written in terms of l, d, and θ?
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Static equilibrium | Uniform sphere on incline | Determining friction
Replies
43
Views
2K
Determine the maximum ratio h/b
Replies
1
Views
2K
Minimum mass of a block
Replies
22
Views
228
Two bodies connected with an elastic thread moving with friction
Replies
6
Views
1K
Maximum allowable value of a force
Replies
5
Views
1K
Minimum force before a system of two blocks will move
Replies
6
Views
2K
Statics and friction -- Two articulated rods connected to blocks
Replies
13
Views
2K
Minimum and maximum values so the system remains at rest
Replies
11
Views
5K
Static friction coefficient for a crate in the back of a truck
Replies
6
Views
2K
Maximum angle reached by a cube placed inside a spinning cylinder
Replies
22
Views
2K

Hot Threads

Recent Insights

Back
Top