Find the tension in each of the cords

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To find the tension in two cords supporting a 10 kg mass at angles of 30 degrees and 45 degrees, one must analyze the forces in both the x and y directions. The equations for the sum of forces in each direction can be established, leading to two equations that represent the system. By manipulating these equations, the tensions in the cords can be solved using a system of equations. The approach emphasizes the importance of balancing forces to determine the unknown tensions. This method provides a systematic way to solve tension problems in physics.
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tension problem...please help!

Homework Statement



A mass of 10 kg is suspended from a ceiling by teo cords that make angles of 30 deg an 45 deg with the ceiling. Find the tension in each of the cords?

Homework Equations



something like t1 cos(30) = t2cos(45)

The Attempt at a Solution



something like t1 cos(30) = t2cos(45)
please help me with this
thankyou
 

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What do you know about the net force in the x and y directions?

I would start by writing a sums of forces equation for the x direction and a sums of forces equation for the y direction. From here, see what you can algebraically manipulate to get what you want.
 
get 2 equations, sum of forces in x, sum of forces in y.

and solve for your 2 unknown tensions by system of equations
 
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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