Final answer:
a. Calculate gravitational potential energy b. Determine tension in the string c. Analyze the motion of the airplane d. Explore equilibrium conditions
Step-by-step explanation:
a. To calculate the gravitational potential energy of the toy airplane, we can use the formula: gravitational potential energy = mass x acceleration due to gravity x height. Here, the mass of the toy airplane is 0.075 kg, the acceleration due to gravity is approximately 9.8 m/s², and the height is the distance from the ceiling. Substitute these values into the formula to find the gravitational potential energy.
b. The tension in the string can be calculated using the formula: tension = gravitational force + centripetal force. Gravitational force can be calculated using the formula: gravitational force = mass x acceleration due to gravity. Centripetal force can be calculated using the formula: centripetal force = mass x velocity² / radius. Substitute the given values into the formulas to find the tension in the string.
c. The motion of the airplane can be analyzed using the principles of free fall. When the airplane is released, it will fall towards the ground due to the force of gravity. The motion can be described using equations of motion, such as the equation: height = initial height + initial velocity x time + 0.5 x acceleration x time². Substitute the values into the equation to find the height of the airplane at any given time.
d. Equilibrium conditions can be explored by considering the forces acting on the airplane. For equilibrium, the net force acting on the airplane must be zero. This means that the gravitational force pulling the airplane downward is balanced by the tension force in the string pulling the airplane upward.