Question

100 points!!! Please help!!!

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.

Answer 1

Answer:

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.

Answer 2

The maximum angle the pendulum makes with the vertical is 41°.

The total energy of the pendulum = maximum kinetic energy (at mean position or bottom) = maximum potential energy (at the highest point)

½ mv² = mgh,  where h is the maximum height of point A from point B

h = L − Lcosθ,  where L = 1.2 m and θ is the maximum angle

½ v² = gh

h = v²/(2g)

h = (2.4 m/s)² / (2 × 9.8 m/s²)

h = 0.294 m

Now to calculate the value of the angle

h = L − Lcosθ

cos θ = (L − h) / L

cos θ = (1.2 − 0.294) / 1.2

θ = 41.0°

The pendulum makes a maximum angle of 41° with the vertical.

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