A 6470 kg helicopter accelerates upward at 0.57 m/s2 while lifting a 1180 kg frame at a construction site
(a) What is the lift force exerted by the air on the helicopter rotors?
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?
(c) What force does the cable exert on the helicopter?
To find the answers to these questions, we can use Newton's laws of motion. Let's go step by step.
(a) What is the lift force exerted by the air on the helicopter rotors?
According to Newton's second law of motion, the net force acting on an object is equal to its mass multiplied by its acceleration (F = m * a). In this case, the upward acceleration of the helicopter also represents the net force acting on the helicopter, which is equal to the lift force generated by the rotors minus the weight of the helicopter and the frame.
The weight of an object can be calculated by multiplying its mass by the acceleration due to gravity, which is approximately 9.8 m/s². Therefore, the weight of the helicopter is given by W_h = m_h * g, where m_h is the mass of the helicopter.
Given:
Mass of the helicopter, m_h = 6470 kg
Upward acceleration, a = 0.57 m/s²
First, calculate the weight of the helicopter:
W_h = m_h * g
W_h = 6470 kg * 9.8 m/s²
Next, calculate the lift force generated by the rotors:
Lift force = Net force = m_h * a + W_h
Substitute the values:
Lift force = 6470 kg * 0.57 m/s² + (6470 kg * 9.8 m/s²)
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?
To find the tension in the cable, we need to consider the forces acting on the frame. The frame experiences two forces - the tension in the cable pulling it upward and the weight of the frame pulling downward. At equilibrium, these two forces balance each other out.
Since the frame is not accelerating vertically, the net force acting on it is zero. Therefore, the tension in the cable is equal to the weight of the frame.
Given:
Mass of the frame, m_f = 1180 kg
Acceleration due to gravity, g = 9.8 m/s²
Tension in the cable = Weight of the frame = m_f * g
Substitute the values to find the tension in the cable.
(c) What force does the cable exert on the helicopter?
The force exerted by the cable on the helicopter is equal in magnitude and opposite in direction to the tension in the cable pulling upward on the frame. Therefore, it is equal to the tension in the cable.