How Do You Calculate Elevator Cable Tension for Maximum Acceleration?

AI Thread Summary
To calculate the elevator cable tension for maximum acceleration, the problem involves an elevator with a mass of 4850 kg and a maximum acceleration of 0.068 m/s². The required equations include Force = mass × acceleration and Forcevertical = Ftens + Fgrav. The initial calculation yields a force of 329.8 N, but this does not account for gravitational force, which is approximately 47530 N. The minimum force must support gravity, while the maximum force must also account for the upward acceleration. Clarification is needed on the definitions of Forcevertical and the net force in the context of the problem.
yandereni
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1. The problem statement, all variables and given/known data
An elevator(4850kg) is to be designed so that the maximum acceleration is 0.068m/s2. What are the minumum and maximum forces the motor must exert on the supporting cable?

2. Homework Equations
Force = mass(acceleration)
Forcevertical = Ftens + Fgrav

The Attempt at a Solution



Forcevertical = Ftens + Fgrav
Force = 4850kg(0.068m/s2)
= 329.8N

Forcevertical = 329.8N - 47530N
= -47200N

I'm not so sure about both answers but i think the first solution is kinda right?

thanks in Advance!
 
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Not quite. Think about what is happening. It also has to account for the force of gravity. So the minimum amount of force needed would be to support the force of gravity, and the maximum would be to not only support the force of gravity, but to accelerate the elevator upward at 0.068m/s2. So How would you express those forces with mathematics?
 
yandereni said:
Forcevertical = Ftens + Fgrav
Please define what Forcevertical represents.
yandereni said:
Force = 4850kg(0.068m/s2)
Which of the forces in the first equation corresponds to "Force" in this equation?
 
haruspex said:
Please define what Forcevertical represents.

Forcevertical means forces on the y-axis

haruspex said:
Which of the forces in the first equation corresponds to "Force" in this equation?
Ftens is the one that corresponds to "Force"
 
yandereni said:
Forcevertical means forces on the y-axis
No, there are two applied forces (plural) on the y axis, and you have those on the right hand side of the equation. Forcevertical is one force. The word I'm looking for is 'net' force, or 'resultant' force.
yandereni said:
Ftens is the one that corresponds to "Force"
Then that's where you are wrong. In the standard equation F=ma, what does F represent? Yes, I know it's a force, but exactly what force?
 
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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