When empty, a particular helicopter of mass 3770 kg can accelerate straight upward at a maximum acceleration of 1.36 m/s2. A careless crewman overloads the helicopter so that it is just unable to lift off. What is the mass of the cargo?
maxthrust= 3770*1.36 figure that out.
Then
maxthrust= mg+ma where a is zero, figure out what the Mass m is.
To solve this problem, we need to consider the forces acting on the overloaded helicopter.
First, let's determine the force needed to lift the empty helicopter. We can use Newton's second law of motion, which states that the force (F) acting on an object is equal to the mass (m) multiplied by the acceleration (a): F = m * a.
In this case, the acceleration (a) is the maximum acceleration that the helicopter can achieve when empty, which is given as 1.36 m/s^2.
F = m * a
F = 3770 kg * 1.36 m/s^2
F = 5127.2 N
So, the force needed to lift the empty helicopter is 5127.2 N.
Now, let's consider the overloaded helicopter. Since it is unable to lift off, the force acting on it is equal to its weight.
The weight of an object can be calculated using the formula: Weight = mass * gravitational acceleration (w = m * g).
Assuming the gravitational acceleration is approximately 9.8 m/s^2, we can use this formula to calculate the weight of the overloaded helicopter:
5127.2 N = (3770 kg + m) * 9.8 m/s^2
Now, we can solve this equation to determine the mass (m) of the cargo:
5127.2 N = (3770 kg + m) * 9.8 m/s^2
Rearranging the equation, we get:
m = (5127.2 N / 9.8 m/s^2) - 3770 kg
m = 527 kg
Therefore, the mass of the cargo is approximately 527 kg.