As the pendulum swings through the origin, it has a speed of v0 = 1.1 m/s. If the mass on the end of the pendulum is 15 g, and the pendulum is 30 cm long, how high does the pendulum swing before coming back down? What is the angle corresponding to that height?

1: 6.18 cm

2: 52.5609 degrees

Explanation:

We have the pendulum speed at the origin, and in that moment, all energy is kinetic, so we can calculate the pendulum energy by:

Ec = 0.5*m*v^2 = 0.5*0.015*1.1^2 = 0.0091 J

Now with that energy, we can calculate the height the pendulum will reach, as in that moment, the kinetic energy is totally converted to gravitational potencial energy:

Eg = m*g*h = 0.0091

0.015 * 9.81 * h = 0.0091

h = 0.0091 / (0.015 * 9.81 ) = 0.0618 m = 6.18 cm

Looking at the image attached, we can see that the pendulum will form a triangle, and one of the cathetus will be the length of the pendulum minus the height it went up, and the hypotenusa will be the pendulum length.

So, we know that the sine of the angle will be the division between the opposite cathetus and the hypotenusa:

sin(angle) = (30-6.18)/30 = 23.82/30 = 0.794 -> angle = 52.5609 degrees

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