 #1
valentina
 3
 2
 Homework Statement:

An object of mass m is being held by a spring without mass and with constant k, which at the same time is attached to a inextensible rope without mass, attached to the ceiling.
At first the spring is at its natural length, and it's released with no velocity.
Find the maximum value for the tension of the rope.
 Relevant Equations:

$$F=kx$$ (elastic force)
$$E_i=E_f$$
I'm having trouble with this problem, I think I solved it but I don't know if what I did is right...
At first when the velocity is 0 and the spring is at its natural length, there's just gravitational potential energy, so $$E_i=mgh$$
And then, when the mass is released and then reaches its minimum height (I choose $$h=0$$ for this case), it only has elastic potential energy and for a moment it doesn't have kinetic energy (right?), so that must be $$E_f=\frac{kh^2}{2}$$
By the the theorem of conservation of mechanical energy, we have $$E_i=E_f$$, then $$mgh=\frac{kh^2}{2}$$, so $$kh=2mg$$
Then I draw the free body diagram for both the mass and for the spring, here's where I don't know if what I did was right:
Where $$\vec{F}$$ is the elastic force
The equations I get are $$F=mg$$ and $$T=F$$ (because at that moment $$\vec{a}=0$$ ?)and this is where starts my confusion:
If I only use those two equations, I get that $$T=mg$$ BUT if I take into account the energy equation, I get that $$F=kh=2mg$$, and then $$T=2mg$$.
What would be the correct way to solve this problem? I'm really confused with the equations I got...
At first when the velocity is 0 and the spring is at its natural length, there's just gravitational potential energy, so $$E_i=mgh$$
And then, when the mass is released and then reaches its minimum height (I choose $$h=0$$ for this case), it only has elastic potential energy and for a moment it doesn't have kinetic energy (right?), so that must be $$E_f=\frac{kh^2}{2}$$
By the the theorem of conservation of mechanical energy, we have $$E_i=E_f$$, then $$mgh=\frac{kh^2}{2}$$, so $$kh=2mg$$
Then I draw the free body diagram for both the mass and for the spring, here's where I don't know if what I did was right:
Where $$\vec{F}$$ is the elastic force
The equations I get are $$F=mg$$ and $$T=F$$ (because at that moment $$\vec{a}=0$$ ?)and this is where starts my confusion:
If I only use those two equations, I get that $$T=mg$$ BUT if I take into account the energy equation, I get that $$F=kh=2mg$$, and then $$T=2mg$$.
What would be the correct way to solve this problem? I'm really confused with the equations I got...