Translational Equilibrium Practice problem

AI Thread Summary
The discussion centers on resolving a translational equilibrium practice problem. A participant identified a mistake in their calculations related to the force of the rope vector. They clarified that the correct frictional forces should be 180 degrees in the x-axis and 90 degrees in the z-axis. Additionally, the correct normal force values are 90 in the x-axis and 0 in the z-axis. The conversation emphasizes the importance of accurate vector considerations in solving equilibrium problems.
hraghav
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Homework Statement
So I am basically stuck at one of the practice problems. The questions states that: A box of mass 𝑀=52.9kg is on a rough surface. It is being pulled by a force of magnitude 𝑇 at an angle of 𝜃=18.4 degrees with the horizontal. The box has a coefficient of static friction 𝜇=0.393 with the surface. What is the angle the force of friction makes with the positive x-axis and positive z-axis? What is the angle the normal force makes with the positive x-axis and positive z-axis?
Relevant Equations
So for frictional force angles I tried to do 180 - 18.4 = 161.6 degrees for x axis as frictional force is in the opposite direction of the force applied and z axis is 18.4. For normal force x axis I did 18.4 and z axis I did 90-18.4. But I got all of them wrong not sure what I am doing wrong. Could someone please help me with this. I have also attached a picture for the problem for reference. Thank you!
Screenshot 2024-02-18 at 7.23.08 PM.png
 
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Thank you I did find my mistake, I was considering the force of rope vector for my calculations. which was not the right way. The correct answer for the frictional forces was 180 degree in x axis and 90 in the z axis and for normal force was 90 x axis and 0 in the z axis!
 
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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