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

6000 + 2500 = 8500 kg = m

m g = weight = 9.81 * 8500

F = weight + m a
F = 9.81* 8500 + .5 * 8500 = 87,635 N

T = 9.81*2500 + .5 * 2500 = 25,775 N

Well, in this rescue scene, the helicopter seems to be working hard to lift that heavy piece of concrete. Let's crunch some numbers here.

To find the upward force exerted by the rotors of the helicopter, we can use Newton's second law: Force = Mass x Acceleration. In this case, the mass being accelerated upwards is the sum of the helicopter's mass (6000 kg) and the mass of the concrete (2500 kg). So, the total mass is 6000 kg + 2500 kg = 8500 kg.

Now, plugging that into the equation, we get:
Force = Mass x Acceleration
Force = 8500 kg x 0.50 m/s^2
Force = 4250 N

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

As for the tension in the cable attaching the concrete to the helicopter, we need to consider the net force acting on the concrete. The net force is equal to the mass of the concrete multiplied by its acceleration (which is the same as the helicopter's acceleration, since they are being lifted together).

So, using the same mass and acceleration as before (2500 kg and 0.50 m/s^2, respectively), we find:
Tension = Mass x Acceleration
Tension = 2500 kg x 0.50 m/s^2
Tension = 1250 N

Hence, the tension in the cable attaching the concrete to the helicopter is 1250 Newtons.

I hope that answered your question and brought a smile to your face!

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

The mass of the helicopter is given as 6000 kg, and the acceleration is given as 0.50 m/s^2. Therefore, the upward force exerted by the rotors of the helicopter can be calculated as:

Force = Mass * Acceleration
Force = 6000 kg * 0.50 m/s^2
Force = 3000 N

So, the upward force exerted by the rotors of the helicopter is 3000 Newtons.

Next, let's calculate the tension in the cable attaching the concrete to the helicopter.

To do this, we need to consider the forces acting on the concrete. There are two forces at play: the force of gravity pulling the concrete downwards and the tension force pulling the concrete upwards.

The force of gravity on the concrete can be calculated using the equation:

Force of Gravity = Mass * Gravitational Acceleration

The mass of the concrete is given as 2500 kg, and the gravitational acceleration is approximately 9.8 m/s^2. Thus, the force of gravity on the concrete is:

Force of Gravity = 2500 kg * 9.8 m/s^2
Force of Gravity = 24500 N

Since the concrete is being lifted upwards, the tension force in the cable must be equal to the force of gravity plus the force exerted by the rotors of the helicopter. Therefore:

Tension Force = Force of Gravity + Force exerted by the rotors
Tension Force = 24500 N + 3000 N
Tension Force = 27500 N

So, the tension in the cable attaching the concrete to the helicopter is 27500 Newtons.

To find the upward force exerted by the rotors of the helicopter and the tension in the cable attaching the concrete, we need to use Newton's second law of motion.

1. Calculate the upward force exerted by the rotors:
The force exerted by the rotors of the helicopter is equal to the sum of the weight of the helicopter and the weight of the concrete, since the net force must provide the necessary acceleration.

Weight of the helicopter = mass of the helicopter * acceleration due to gravity
Weight of the helicopter = 6000 kg * 9.8 m/s^2

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

Upward force exerted by the rotors = Weight of the helicopter + Weight of the concrete

2. Calculate the tension in the cable attaching the concrete:
The tension in the cable is the force exerted by the helicopter to lift the concrete. It is equal to the weight of the concrete.

Tension in the cable = Weight of the concrete

Now, let's calculate the values:

Weight of the helicopter = 6000 kg * 9.8 m/s^2 = 58800 N

Weight of the concrete = 2500 kg * 9.8 m/s^2 = 24500 N

Upward force exerted by the rotors = 58800 N + 24500 N = 83300 N

Tension in the cable = 24500 N

Therefore, the upward force exerted by the rotors of the helicopter is 83300 Newtons, and the tension in the cable attaching the concrete to the helicopter is 24500 Newtons.