100 ! !

suppose the pendulum in the figure has a mass of 0.34 kg and is moving to the right at point b with a speed of 2.4 m/s. air resistance is negligible.

find the maximum angle the string makes with the vertical as the bob swings back and forth. ignore air resistance.

41°

Explanation:

Kinetic energy at bottom = potential energy at top

½ mv² = mgh

½ v² = gh

h = v²/(2g)

h = (2.4 m/s)² / (2 × 9.8 m/s²)

h = 0.294 m

The pendulum rises to a height of  above the bottom.  To determine the angle, we need to use trigonometry (see attached diagram).

L − h = L cos θ

cos θ = (L − h) / L

cos θ = (1.2 − 0.294) / 1.2

θ = 41.0°

Rounded to two significant figures, the pendulum makes a maximum angle of 41° with the vertical.

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