Calculate Upward Force & Tension for Helicopter & Truck

[saber1357]

Homework Statement

A 15,000 kg helicopter lifts a 4500 kg truck with an upward acceleration of 1.4 m/s2.
Calculate (a) the net upward force on the helicopter blades from the air and (b) the tension in
the cable between helicopter and truck.

Homework Equations

T = mg

The Attempt at a Solution

I was able to calculate the upward force, but I am having difficulty finding out how to calculate the tension. I know that the truck is pulling the heli with the force of gravity, and the helicopter is pulling the truck with the upward force. But how do I relate the two?

 

[Hootenanny]

Hint: If the truck was sat on the [frictionless] ground, how much force would be required to accelerate it at 1.4m.s^-2? What is the weight of the truck? How do you sum forces?

 

[m2003]

To calculate the tension in the cable between the helicopter and truck, we can use Newton's second law, which states that the net force on an object is equal to its mass times its acceleration. In this case, the net force on the truck is equal to its mass (4500 kg) times its acceleration (1.4 m/s2). This gives us a net force of 6300 N on the truck.

Since the cable is connected to both the helicopter and the truck, this net force must also be acting on the helicopter. Therefore, the tension in the cable is equal to the net force on the helicopter, which we can calculate using the same formula. The net force on the helicopter is equal to its mass (15,000 kg) times its acceleration (1.4 m/s2), which gives us a net force of 21,000 N.

So, the tension in the cable between the helicopter and truck is 21,000 N. This means that the helicopter is pulling the truck with a force of 21,000 N, while the truck is pulling the helicopter with a force of 6300 N (due to the force of gravity).