Newton's law problem: Helicopter lifting a box with a rope

[Stell]

Homework Statement

A helicopter is carrying a box ( mass= 400kg) with a rope that can stand 5000N
a) what is the biggest acceleration that can the helicopter have (going upwards)
b)how should the helicopter move (upwards or downwards and with a=?) if the rope can stand only 3000N?

Relevant Equations

F=ma

Forces:
Box--> W(weight) and T(tension)
Rope-->T1(reaction of T) and T2(because of the helicopter)

So first i calculated Weight:
W=mg=400*10=4000N
In order to find the acceleration i should use Newton's 2nd law so:
(Box) : T - W = ma
T - 4000=400a

The problem is with the rope. We can exert 5000N to the rope. So, does this mean that T2 -T1= 5000?
And how can this help me since i don't know anything about T2.
At first i just thought that T1=5000 N, so since T1=T i calculated that
T - 4000=400a => a=2.5 m/s²
But then i realized that there is also another force applied to the rope (T2). So how can this be solved now?Can someone help me?

 

[Chestermiller]

The tension without acceleration is T = mg = 4000 N. If the rope is just going to fail, its tension with acceleration is going to have to be T = 5000 N.

 

[Stell]

The tension without acceleration is T = mg = 4000 N. If the rope is just going to fail, its tension with acceleration is going to have to be T = 5000 N.

Thank you for your reply. So, if i understand, that means a=2.5 m/s² ?

 

[Chestermiller]

Thank you for your reply. So, if i understand, that means a=2.5 m/s² ?

Sure.

 

[kuruman]

But then i realized that there is also another force applied to the rope (T2). So how can this be solved now?

There is no other force. If you solve the equation T - W = ma for the tension, you get
T = W + ma
Think of this expression as giving you the tension T in the rope when the acceleration is a for fixed weight W.
If you put in numbers, you get
T = 4000 N + (400 kg)*a
When the acceleration is zero, the tension is T = 4000 N.
When the acceleration is 1 m/s², the tension is T = 4400 N.
When the acceleration is 2.5 m/s², the tension is T = 5000 N.
When the acceleration is greater than 2.5 m/s², the rope breaks regardless of the value of the acceleration.

 

[Stell]

There is no other force. If you solve the equation T - W = ma for the tension, you get
T = W + ma
Think of this expression as giving you the tension T in the rope when the acceleration is a for fixed weight W.
If you put in numbers, you get
T = 4000 N + (400 kg)*a
When the acceleration is zero, the tension is T = 4000 N.
When the acceleration is 1 m/s², the tension is T = 4400 N.
When the acceleration is 2.5 m/s², the tension is T = 5000 N.
When the acceleration is greater than 2.5 m/s², the rope breaks regardless of the value of the acceleration.

Thank you for your explanation!