Calculating Mass Using Forces and Acceleration

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To calculate the mass of the octagon under the influence of two equal forces, one must first determine the resultant force vector from the applied forces. The forces are 0.5 N each, directed north and southeast, which can be combined to find the total force. The acceleration of 0.3 m/s² is given, allowing the use of Newton's second law (F = m*a) to solve for mass. There is no need to decompose the acceleration vector, as the magnitude of the resultant force is sufficient for the calculation. This approach will yield the mass of the object effectively.
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Homework Statement


An octagon is on a table with no friction. There are two equal forces which are put on two faces of the octagon, one in direction of the north, the other in direction of the south-east. These forces are all 0,5 N. If the module of the acceleration is 0,3 m/s^2, what is the mass of the object.

Homework Equations


Sum of Force of y = m * a in y

Sum of Force of x = m a in x

The Attempt at a Solution


I know that I must decompose my south-east forces and find its component. What I don't understand is how to find the components of the acceleration to be able to do my calculations. Could somebody give me a hint ?
 
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You don't need to decompose the acceleration. You need to find the magnitude of the Force vector that is the vector sum of the two applied forces. Then you can use that and the given magnitude of acceleration to find the mass.
 
andrewkirk said:
You don't need to decompose the acceleration. You need to find the magnitude of the Force vector that is the vector sum of the two applied forces. Then you can use that and the given magnitude of acceleration to find the mass.
Oh ok, I'll try it and see what it gives.
 
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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