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

In summary, the conversation discusses forces involved in a situation where a box is being lifted by a helicopter using a rope. The forces include weight and tension acting on the box, and tension in the rope due to the reaction of the tension exerted by the helicopter. The solution involves using Newton's 2nd law to calculate acceleration and determining the necessary tension in the rope for it to not break.
  • #1
Stell
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3
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?
 

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  • #2
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.
 
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  • #3
Chestermiller said:
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 ?
 
  • #4
Stell said:
Thank you for your reply. So, if i understand, that means a=2.5 m/s² ?
Sure.
 
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  • #5
Stell said:
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.
 
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  • #6
kuruman said:
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!
 
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1. What is Newton's law problem about a helicopter lifting a box with a rope?

Newton's law problem involves the application of Newton's laws of motion to analyze the forces acting on a helicopter as it lifts a box with a rope. This problem helps us understand the principles of motion and how forces affect the movement of objects.

2. What are the three laws of motion in Newton's law problem?

The three laws of motion in Newton's law problem are: 1) The law of inertia, which states that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force. 2) The law of acceleration, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. 3) The law of action and reaction, which states that for every action, there is an equal and opposite reaction.

3. How does the weight of the box affect the helicopter in Newton's law problem?

The weight of the box affects the helicopter in Newton's law problem by creating a downward force (gravity) that must be countered by the upward force of the helicopter's rotors. This requires the helicopter to exert more force to lift the box, which can affect its overall stability and movement.

4. How does the length of the rope affect the forces in Newton's law problem?

The length of the rope affects the forces in Newton's law problem by changing the angle at which the rope pulls on the box. A longer rope will create a smaller angle, resulting in a smaller horizontal component of the force and a larger vertical component. This can affect the balance of forces and the overall movement of the helicopter and box.

5. What other factors besides the weight of the box and the length of the rope can affect the helicopter's ability to lift the box in Newton's law problem?

Other factors that can affect the helicopter's ability to lift the box in Newton's law problem include the strength and power of the helicopter's rotors, the mass and shape of the box, and any external forces such as wind or air resistance. Additionally, the skill and experience of the pilot can also play a role in successfully lifting the box with the helicopter.

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