Question

1. You released a pendulum of mass 1kg from a height of 0.05m

b. If the pendulum loses 18% of the initial energy by the time it reaches the bottom, how fast is it going when it reaches the bottom?
c. If the pendulum loses another 7% of its remaining energy by the time it reaches the other side, how high up does it go?
d. After a few minutes the pendulum is no longer swinging at all, explain why this happens in terms of energy?​

Answer 1

To find the speed of the pendulum when it reaches the bottom after losing 18% of its initial energy, we can use the principle of conservation of energy.

Step-by-step explanation:

To find the speed of the pendulum when it reaches the bottom after losing 18% of its initial energy, we can use the principle of conservation of energy. The initial potential energy of the pendulum is equal to the sum of its final kinetic energy and the energy lost. The potential energy at the initial height can be calculated as mgh, where m is the mass, g is the acceleration due to gravity, and h is the initial height.

Given:

• Mass (m) = 1 kg
• Initial height (h) = 0.05 m
• Energy lost = 18% = 0.18

The potential energy at the initial height is calculated as:

PE = mgh = (1 kg)(9.8 m/s²)(0.05 m) = 0.49 J

The final kinetic energy is the total energy remaining after the loss:

KE = (1 - 0.18) x 0.49 J = 0.4022 J

The speed of the pendulum when it reaches the bottom is equal to the square root of twice the kinetic energy divided by the mass:

Speed = √(2 x KE / m) = √(2 x 0.4022 J / 1 kg) = 0.635 m/s.