When empty, a particular helicopter of mass 3770 kg can accelerate straight upward at a maximum acceleration of 1.34 m/s2. A careless crewman overloads the helicopter so that it is just unable to lift off. What is the mass of the cargo?
To find the mass of the cargo, we need to determine the additional mass that causes the helicopter to be unable to lift off.
Let's assume the mass of the cargo is "m" kg.
When the helicopter is empty, it can accelerate straight upward at a maximum acceleration of 1.34 m/s^2. This means that the net force acting on the empty helicopter is equal to its mass multiplied by this maximum acceleration.
The net force (F_net) can be calculated using Newton's second law of motion:
F_net = m_empty * a_max
Here, m_empty is the mass of the empty helicopter, given as 3770 kg, and a_max is the maximum acceleration, given as 1.34 m/s^2.
Next, we need to calculate the net force on the overloaded helicopter. Since it is unable to lift off, the net force acting on it is zero. The weight of the overloaded helicopter (including the cargo) is equal to the force of gravity acting on it:
F_gravity = m_overloaded * g
Here, m_overloaded is the mass of the overloaded helicopter (including the cargo) and g is the acceleration due to gravity, which is approximately 9.8 m/s^2.
Since the net force acting on the overloaded helicopter is zero, we can equate the net force and the force of gravity:
m_empty * a_max = m_overloaded * g
Now we can solve this equation for the mass of the cargo (m):
m = (m_empty * a_max) / g
Let's substitute the given values into the equation and calculate the mass of the cargo:
m = (3770 kg * 1.34 m/s^2) / 9.8 m/s^2
m ≈ 515.44 kg
Therefore, the mass of the cargo is approximately 515.44 kg.