What Is the Acceleration and Tension in a Frictionless Inclined Plane System?

AI Thread Summary
The discussion focuses on calculating the acceleration and tension in a frictionless inclined plane system with two equal masses (m1 and m2) of 1.0 kg and an angle θ of 30°. For part A, the user attempts to derive the equations of motion but questions whether to use the quadratic formula for solving the resulting equation. Another participant points out an error in the user's force analysis and suggests reevaluating the forces acting on the system instead of resorting to the quadratic formula. The conversation emphasizes the importance of correctly applying Newton's second law to find the acceleration and tension in the system. Accurate calculations are crucial for understanding the dynamics of inclined plane systems.
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Homework Statement


If m1=m2=1.0 kg and θ=30°, what will be the acceleration of the system? Calculate the tension in the cord, if a block m1 lying on a frictionless inclined plane and is connected to a mass less cord. Assume m1 is moving down the plane for A), and for B) m1 is in the opposite direction. C) If m1= 1 kg and θ=30°, and the system remains at rest, what must the mass of m2 be? Calculate the tension.

Homework Equations



ƩF=ma

The Attempt at a Solution



For part A
I have this so far
m1 x: ƩF=mg(sin30°)-T=ma
T=mg(sin 30°)/ma
y: ƩF=N-mg(cos 30°)=0
N=mg(cos 30°)
m2 y: T-mg=ma
T=ma+mg
T1=T2
therefore, ma+mg=(g(sin 30°))/a
so to solve for a I end up getting
a2+ ga - gsin30°=0
so do I just do the quadratic formula here or am I going the wrong way about it?

Here's the problem if you need to see the picture

http://imageshack.us/f/812/ue4y.jpg/


 
Physics news on Phys.org
No need for the quadratic formula. look at your Forces in the direction. You made a mistake.
 
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}...
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