Pulley System equilibrium problem

AI Thread Summary
To solve the pulley system equilibrium problem, it is essential to establish the free body diagrams (FBD) for both masses involved. The downward force on mass M is identified as F=mg/2, while the tension forces acting on mass m are represented as F=mg. The discussion emphasizes the importance of writing equations based on the FBDs and ensuring that the sum of forces in both the x and y directions equals zero. By analyzing these forces, one can derive the necessary tensions to demonstrate that tan(Theta) = 1 + (2M/m). Understanding these components is crucial for solving the equilibrium condition effectively.
Dcarroll
Messages
7
Reaction score
0

Homework Statement



If the system below is in equilibrium, show that tan(Theta) = 1 + (2M/m)

View attachment Doc1.doc

Homework Equations



F=ma

The Attempt at a Solution



I was pretty confused with this problem. All I think I know is that the force being pulled downward on M is F=mg/2. Can someone explain to me how to solve the next part?
 
Physics news on Phys.org
Dcarroll said:

Homework Statement



If the system below is in equilibrium, show that tan(Theta) = 1 + (2M/m)

View attachment 29838

Homework Equations



F=ma

The Attempt at a Solution



I was pretty confused with this problem. All I think I know is that the force being pulled downward on M is F=mg/2. Can someone explain to me how to solve the next part?

Can you post your Free Body Diagram (FBD) sketches of the two masses for this problem? That's usually a good first step in this type of problem.
 
Ok I tried drawing the free body diagrams for the masses-

View attachment Doc1.doc
 
Dcarroll said:
Ok I tried drawing the free body diagrams for the masses-

View attachment 29854

That's a start. I don't think you can write the upper right vector on M just yet, though. Now, for each FBD, what equations do you write, and how do you use them to solve for the tensions?
 
Well don't I have the equations in my FBD? For example the tension force caused by "m" is F=mg, and the two tensions for the strings holding "m" up are F=mg/2? I am just confused on what to do next. We have never done any problems like this
 
Dcarroll said:
Well don't I have the equations in my FBD? For example the tension force caused by "m" is F=mg, and the two tensions for the strings holding "m" up are F=mg/2? I am just confused on what to do next. We have never done any problems like this

I was thinking of the component-wise sums of forces. The Fx and Fy sums need to each sum to zero, right? That should be how you can work out the final tensions, especially for mass M.
 

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

3 pulley problem with attached masses
Replies
15
Views
6K
Problem with pulleys - two fixed and one movable
Replies
22
Views
371
System of two pulleys and three masses
Replies
22
Views
6K
Finding acceleration of the pulley block system
Replies
23
Views
3K
A spring, disk and pulley system
Replies
40
Views
4K
Ideal Vs Real Mass Pulley system
Replies
10
Views
5K
System with Pulleys and a Rope That Might Break
Replies
26
Views
2K
How Do You Solve a Non-Equilibrium Pulley System with a 154 Degree Angle?
Replies
10
Views
701
Pulley system to balance the weight of a person
Replies
7
Views
2K
Pulley system -- Calculate the mass that balances this pulley system
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top