A simple pendulum has a mass of 0.27 kg and a length of 1.5 m. It is displaced through an angle of 40° and then released. After a time, the maximum angle of swing is only 14°. How much energy has been lost to friction?​Select one:a.0.81 Jb.0.93 Jc.0.12 Jd.1.00 Je.1.05 J

The energy of a pendulum is given by the formula:

E = mgh

where: m is the mass of the pendulum, g is the acceleration due to gravity, and h is the height of the pendulum.

The height of the pendulum can be calculated using the formula:

h = l - l*cos(θ)

where: l is the length of the pendulum, and θ is the angle of displacement.

First, we calculate the initial energy of the pendulum when it is displaced through an angle of 40°.

h1 = 1.5 m - 1.5 m * cos(40°) = 0.485 m

E1 = 0.27 kg * 9.8 m/s² * 0.485 m = 1.28 J

Next, we calculate the final energy of the pendulum when the maximum angle of swing is only 14°.

h2 = 1.5 m - 1.5 m * cos(14°) = 0.037 m

E2 = 0.27 kg * 9.8 m/s² * 0.037 m = 0.098 J

The energy lost to friction is the difference between the initial and final energy.

ΔE = E1 - E2 = 1.28 J - 0.098 J = 1.18 J

However, this answer is not in the options. Please check the values or the options.

The energy of a pendulum is given by the formula:

E = mgh

where: m is the mass of the pendulum, g is the acceleration due to gravity, and h is the height of the pendulum.

The height of the pendulum can be calculated using the formula:

h = l - l*cos(θ)

where: l is the length of the pendulum, and θ is the angle of displacement.

First, we calculate the initial energy of the pendulum when it is displaced through an angle of 40°.

h1 = 1.5 m - 1.5 m * cos(40°) = 0.485 m

E1 = 0.27 kg * 9.8 m/s² * 0.485 m = 1.28 J

Next, we calculate the final energy of the pendulum when the maximum angle of swing is only 14°.

h2 = 1.5 m - 1.5 m * cos(14°) = 0.037 m

E2 = 0.27 kg * 9.8 m/s² * 0.037 m = 0.098 J

The energy lost to friction is the difference between the initial and final energy.

ΔE = E1 - E2 = 1.28 J - 0.098 J = 1.18 J

However, this answer is not in the options. There might be a mistake in the calculation or the provided options. Please check the question and the provided options again.