Question

The swinging pendulum has 10 joules of potential energy at its maximum height at points (1) and (5). If the mass of the pendulum is 10kg, how fast is the pendulum moving at point (3)?

Answer 1

The speed of the pendulum at point 3 is 1.4 m/s

Explanation:

We can solve this problem by using the law of conservation of energy. In fact, the mechanical energy of the pendulum (which is the sum of his potential energy + his kinetic energy) must be conserved. So we can write:

$U_1 +K_1 = U_3 + K_3$

where

$U_1$ is the initial potential energy, at the highest position

$K_1$ is the initial kinetic energy, at the highest position

$U_3$ is the final potential energy, at the lowest position

$K_3$ is the final kinetic energy, at the lowest position

We are told that:

$U_1 = 10 J$ is the potential energy of the pendulum at the maximum height

$K_1 = 0$ (when the pendulum is at maximum height, the speed is zero, so the kinetic energy is zero)

$U_3 = 0$ (potential energy is zero at the lowest position)

Therefore,

$K_3 = U_1 = 10 J$

Kinetic energy can be rewritten as

$K_3 = \frac{1}{2}mv^2$

where

m = 10 kg is the mass of the pendulum

v is its speed at point 3

Solving for v,

$v=\sqrt{\frac{2K_3}{m}}=\sqrt{\frac{2(10)}{10}}=1.4 m/s$

Learn more about kinetic energy:

brainly.com/question/6536722

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