Dynamics question -- 3 masses on a pulley-rope system on an inclined plane

AI Thread Summary
The discussion centers on solving a dynamics problem involving three masses on a pulley-rope system on an inclined plane. One participant calculated an acceleration of 4.8 m/s² and tensions T1 and T2 as 24.5N and 34.3N, respectively, but expressed uncertainty about the accuracy of these values. Another participant obtained a lower acceleration of 4.1 m/s² and pointed out that the original calculations neglected the effects of mass accelerations and friction on the tensions. There is a request for clearer equations to facilitate better understanding and commentary on the calculations. The conversation highlights the complexity of the problem and the need for detailed breakdowns of the equations used.
rabsta00
Messages
3
Reaction score
0
Homework Statement
A mass m is 5kg and another mass, M=6kg. Find the acceleration of this system if the kinetic friction is 0.1 and theta = 30 degrees. Find all tensions of connecting ropes. For which values of M will the system stay in an equilibrium position?Assume that the static friction coefficient is 0.15. Disregard the mass of the pulley and ropes.
Relevant Equations
F=ma
Screen Shot 2021-03-29 at 12.31.31 pm.png

This image was provided, I've completed the first part of the question and got a = 4.8m/s^2 as well as T1= 24.5N and T2=34.3N. not sure about my answers though. also I don't understand the mass in static equilibrium part, can anyone explain how to solve that? Thanks.
 
Physics news on Phys.org
rabsta00 said:
got a = 4.8m/s^2
I get a far smaller value. Please post your working.
 
haruspex said:
I get a far smaller value. Please post your working.

IMG_2060.jpg

I tried a different method but ended up getting a = 4.1 which isn't much smaller.
 
You omitted the effect of the mass accelerations and friction on the tensions.
 
rabsta00 said:
View attachment 280501
I tried a different method but ended up getting a = 4.1 which isn't much smaller.
Please take the trouble to type equations in. It makes it much easier to quote lines to comment on.
You have T1=2mg sin(θ)-mg sin(θ). How do you arrive at that?
Your calculation of the acceleration of 2m ignores the string. You just have it sliding down the slope unrestrained.
 
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...
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}...
Back
Top