Final answer:
The change in gravitational potential energy of the pendulum system as it swings from point A to point B is approximately 1.4422 Joules, calculated using the formula GPE = mgh.
Step-by-step explanation:
To determine the change in the gravitational potential energy (GPE) of the pendulum bob-earth system as it swings from its initial position (point A) to the bottom of its arc (point B), we can apply the conservation of mechanical energy principle. GPE is highest at the highest point of swing and is defined as GPE = mgh, where m is the mass of the bob, g is the acceleration due to gravity (9.81 m/s²), and h is the vertical height change.
The height change can be calculated using trigonometry because the pendulum bob descends along the arc of a circle. The initial height (h) from the lowest point can be determined by h = L - L\cos(\theta), where L is the length of the string and \theta is the angle with the vertical. Plugging in the values:
h = 1.5m - 1.5m\cos(39.0°) = 1.5m - 1.5m\times0.777 (cosine of 39.0°) = 1.5m - 1.1655m = 0.3345m.
The change in GPE is:
\Delta GPE = mgh = 0.440kg \times 9.81 m/s² \times 0.3345m = 1.4422 Joules.
Therefore, the change in gravitational potential energy as the pendulum swings from point A to B is approximately 1.4422 Joules.