In a rescue scene during the 911 crisis, a helicopter of mass 6000 kg accelerates upwards at the rate of 0.50 m/s2 while lifting a 2500 kg piece of concrete. What is the upward force exerted by the rotors of the helicopter? What is the tension in the cable attaching the concrete to the helicopter?

I thnk d Tension wil b T=ma+mg..m=max of load.ah may b wrong

2)force of aircraft,F=ma...

To solve this problem, we need to calculate the upward force exerted by the rotors of the helicopter and the tension in the cable attaching the concrete.

1. Find the upward force exerted by the rotors of the helicopter:
- The force exerted by the rotors is equal to the total weight being lifted (helicopter + concrete) plus the force required to accelerate the system.
- Calculate the weight being lifted: Mass of the helicopter + Mass of the concrete
Weight = (Mass of the helicopter + Mass of the concrete) * gravitational acceleration
Weight = (6000 kg + 2500 kg) * 9.8 m/s^2
Weight = 8500 kg * 9.8 m/s^2
Weight = 83300 N
- Calculate the upward force: Weight + Force required to accelerate
Upward force = 83300 N + (Mass of the helicopter + Mass of the concrete) * acceleration
Upward force = 83300 N + (6000 kg + 2500 kg) * 0.50 m/s^2
Upward force = 83300 N + 8500 kg * 0.50 m/s^2
Upward force = 83300 N + 4250 N
Upward force = 87550 N

2. Find the tension in the cable attaching the concrete to the helicopter:
- The tension in the cable is equal to the weight of the concrete minus the force required to accelerate it.
- Calculate the weight of the concrete: Mass of the concrete * gravitational acceleration
Weight of the concrete = 2500 kg * 9.8 m/s^2
Weight of the concrete = 24500 N
- Calculate the tension: Weight of the concrete - Force required to accelerate
Tension = 24500 N - Mass of the concrete * acceleration
Tension = 24500 N - 2500 kg * 0.50 m/s^2
Tension = 24500 N - 1250 N
Tension = 23250 N

Therefore, the upward force exerted by the rotors of the helicopter is 87550 N, and the tension in the cable attaching the concrete to the helicopter is 23250 N.

To find the upward force exerted by the rotors of the helicopter, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.

First, let's find the total mass being lifted by the helicopter. We have the mass of the helicopter (6000 kg) and the mass of the concrete piece (2500 kg), so the total mass is:

Total mass = mass of helicopter + mass of concrete
Total mass = 6000 kg + 2500 kg
Total mass = 8500 kg

Now, we can use the total mass and the acceleration of the helicopter to find the upward force exerted by the rotors:

Force = mass * acceleration
Force = 8500 kg * 0.50 m/s^2
Force = 4250 N

Therefore, the upward force exerted by the rotors of the helicopter is 4250 Newtons.

To find the tension in the cable attaching the concrete to the helicopter, we need to consider the forces acting on the concrete. Since the concrete is being lifted, there are two forces acting on it:

1. The upward force exerted by the rotors of the helicopter, which we just calculated as 4250 N.
2. The downward force due to the weight of the concrete, which is given by the mass of the concrete multiplied by the acceleration due to gravity (9.8 m/s^2).

Weight of concrete = mass of concrete * acceleration due to gravity
Weight of concrete = 2500 kg * 9.8 m/s^2
Weight of concrete = 24500 N

Now, let's calculate the tension in the cable:

Tension in cable = upward force - weight of concrete
Tension in cable = 4250 N - 24500 N
Tension in cable = -20250 N

The negative sign indicates that the tension in the cable is acting downwards, opposing the upward force exerted by the helicopter's rotors. Therefore, the tension in the cable attaching the concrete to the helicopter is 20250 Newtons downward.