A simple pendulum of length 1 m is released when it makes an angle of 6 degrees with the vertical.
Find:
a) The speed at the lowest point;
b)If the mass of the bob is 260 g, what is the total energy?
Thank You
To find the answers to the given questions, we first need to determine the initial conditions of the pendulum.
Given:
Length of the pendulum (l) = 1 m
Angle with the vertical (θ) = 6 degrees
a) To find the speed at the lowest point:
The speed at the lowest point can be determined using the principle of conservation of mechanical energy. The total mechanical energy of a simple pendulum is the sum of its potential energy and kinetic energy.
The potential energy at the highest point, where the pendulum is released, is given by:
PE = m*g*h
where m is the mass of the bob, g is the acceleration due to gravity, and h is the vertical height with respect to the lowest point.
The kinetic energy at the lowest point is given by:
KE = (1/2)*m*v^2
where v is the velocity at the lowest point.
Since the total mechanical energy is constant throughout the motion, we have:
PE + KE = Constant
At the highest point, the pendulum has only potential energy and no kinetic energy, so the total energy is maximum.
At the lowest point, the pendulum has only kinetic energy and no potential energy, so the total energy is minimum.
Therefore, at the lowest point, the total energy is equal to the kinetic energy:
Total Energy = KE
Let's calculate the values.