When empty, a particular helicopter of mass 3770 kg can accelerate straight upward at a maximum acceleration of 1.32 m/s2. A careless crewman overloads the helicopter so that it is just unable to lift off. What is the mass of the cargo?

Available upward thrust = M*(g+a) = 41960 N.

Helicopter weight = M*g = 36,984 N

Added weight that prevents liftoff =
4976 N

Added mass that prevents liftoff = 4976/g = 507 kg

To solve this problem, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration (F = ma).

In this scenario, the maximum acceleration of the helicopter when empty is given as 1.32 m/s^2. However, when it is overloaded, it cannot lift off. This means that the maximum force of the helicopter's engines is equal to the force of gravity acting on the helicopter and cargo combined when it's unable to lift off.

The force of gravity can be calculated using the formula F = mg, where m is the mass of the helicopter and cargo, and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Therefore, the equation becomes:

ma = mg

By canceling out the "m" term on both sides, we get:

a = g

Since we're given the maximum acceleration, which is 1.32 m/s^2, and the acceleration due to gravity is 9.8 m/s^2, we can conclude that 1.32 m/s^2 is equal to 9.8 m/s^2.

Now we can find the mass of the cargo:

m = F/a

We know the maximum force of the helicopter's engines required to lift off is equal to the force of gravity acting on it when unable to lift off. The force of gravity is calculated as the weight of the helicopter and cargo, which is given by the formula:

F = mg

Substituting the known values:

3770 kg * 9.8 m/s^2 = F

Solving for F:

F = 36946 N

Finally, we can determine the mass of the cargo by dividing this force by the acceleration:

m = F / a

m = 36946 N / 1.32 m/s^2

m ≈ 28033.33 kg

Therefore, the mass of the cargo is approximately 28033.33 kg.