Calculating the Force of a Wall on a Wedge

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The discussion centers on calculating the force exerted by a wall on a wedge inclined at angle theta, with a block of mass m sliding down the wedge. The key forces identified are the gravitational force (mg) acting downward, the net force (mg sin theta) along the incline, and the normal force (mg cos theta) between the block and the wedge. The participants note that the wedge is not immobile, which affects the calculations. Ultimately, the derived expression for the force of the wall on the wedge is mg cos theta sin theta. This problem illustrates the complexities of forces in a dynamic system involving inclined planes and external walls.
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Homework Statement


A wedge with an inclination of angle theta rests next to a wall. A block of mass m is sliding down the plane, as shown. There is no friction between the wedge and the block or between the wedge and the horizontal surface. (Intro 1 figure) what is the magnitude of the force of the wall exerts on the wedge?



Homework Equations



I know that the sum of all forces is mg sin theta. and i know that the normal force between the block and wedge is mgcos theta. Please does anyone know the answer

The Attempt at a Solution

 
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the sum of all forces is mg
 
f net would actually be mgsin theta. I am doing the problem right now on an online program and for that part of the problem it said that i got it right. so those are the knowns, mgsintheta for the net forces and mgcos theta for the normal force between the block and the wedge.
 
I think it depends on what you are calling 'all' the forces.

the only outside force acting on the system is gravity and gravity doesn't care about thewedge or anything else. it just acts downward
 
i just rearranged some equations and found that the answer was mgcos@sin@
 
most problems like this consider the wedge to be immobile. therefore one would normally consider the force to be mg sin theta. in this problem the wedge is not immobile.
 
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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