Finding mass given force and acceleration

AI Thread Summary
To find the mass of a woman in a lift accelerating at 2 m/s² with a force of 945 N acting on her, the gravitational force must be considered alongside the upward force. The equation F = ma can be adjusted to account for both forces, leading to the equation 945 - mg - ma = 0. By substituting the acceleration due to gravity (9.81 m/s²) and the lift's acceleration (2 m/s²), the mass can be calculated as m = 945 / (9.81 + 2), resulting in a mass of 80 kg. This approach highlights the importance of formulating the problem mathematically to simplify the solution process. Understanding the interplay of forces is crucial in solving such problems.
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a lift ascends with a uniform acceleration of 2m/s^2 whilst transporting a woman. Calculate her mass if the force exerted on her from the floor was 945N.

ANS: 80KG

I have tried F = MA

M = F/A = 945/2 = 472.5

Inertia may have been taken into account but is this possible without being given the mass?
 
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I hate elevator questions; very tricky!
You have the upward force of 945 N on the lady.
But you forgot gravity also has a grip on her.
Include that, and you will get the 80 kg!
 
I hate them too! how do i include gravity in there? It would usually be the product of her mass and 9.81 but I am not given her mass
 
Write it as mg. You'll have two m's in your F = ma equation but it is not a big problem to collect them as like terms in a linear equation. This is an important idea: write it out even if it strikes you as unsolvable - once it appears in front of you in a mathematical form, a whole different thought process in your mind takes over and often the difficulties disappear.
 
945 - mg - ma = 0
g + a x m = 945
9.81 + 2 x m = 945
m = 945/11.81 = 80kg
Thanks!
 
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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