A pendulum has a mass of 1.5 kg and starts at a height of 0.4 m. If it is released from rest, how fast is it going when it reaches the lowest point of its path? Acceleration due to gravity is g = 9.8 m/s2.
Assuming the lowest point of its path is at a height of 0 m, I would use the concept of conservation of energy:
At the highest point, the pendulum has no kinetic energy since its velocity is zero, so the total energy at that point is:
\(E = mgh\)
At the lowest point the potential energy is zero since the height h = 0, and now the energy reads:
\(E = \frac{1}{2} m v^{2}\)
Since no energy is lost:
\(mgh = \frac{1}{2} m v^{2}\)
Solve for v:
\(v = \sqrt{2gh}\)