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:
[tex]U_1 +K_1 = U_3 + K_3[/tex]
where
[tex]U_1[/tex] is the initial potential energy, at the highest position
[tex]K_1[/tex] is the initial kinetic energy, at the highest position
[tex]U_3[/tex] is the final potential energy, at the lowest position
[tex]K_3[/tex] is the final kinetic energy, at the lowest position
We are told that:
[tex]U_1 = 10 J[/tex] is the potential energy of the pendulum at the maximum height
[tex]K_1 = 0[/tex] (when the pendulum is at maximum height, the speed is zero, so the kinetic energy is zero)
[tex]U_3 = 0[/tex] (potential energy is zero at the lowest position)
Therefore,
[tex]K_3 = U_1 = 10 J[/tex]
Kinetic energy can be rewritten as
[tex]K_3 = \frac{1}{2}mv^2[/tex]
where
m = 10 kg is the mass of the pendulum
v is its speed at point 3
Solving for v,
[tex]v=\sqrt{\frac{2K_3}{m}}=\sqrt{\frac{2(10)}{10}}=1.4 m/s[/tex]
Learn more about kinetic energy:
brainly.com/question/6536722
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