a simple pendulum is made from a bob of mass 0.040 kg suspended on a light on a light string of length 1.4m. keeping the string taut the pendulum is pulled to one side until it has gained height of 0.10m . calculate total energy of the oscillation
m g h = 0.040 * 9.81 * 0.10
What is total energy of the oscillation and amplitude of the resulting oscillation
To calculate the total energy of the oscillation for a simple pendulum, we need to consider the potential energy and the kinetic energy of the system.
1. Calculate the potential energy:
The potential energy of the pendulum is given by the equation:
Potential Energy = m * g * h,
where m is the mass of the bob, g is the acceleration due to gravity, and h is the height of the bob.
Given:
Mass of the bob (m) = 0.040 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Height (h) = 0.10 m
Potential Energy = 0.040 kg * 9.8 m/s^2 * 0.10 m
Potential Energy = 0.0392 J
2. Calculate the kinetic energy:
The kinetic energy of the pendulum is given by the equation:
Kinetic Energy = (1/2) * m * v^2,
where m is the mass of the bob and v is the velocity of the bob.
For a simple pendulum, at the extreme points of its swing, the bob's velocity is zero. Therefore, at the highest point, the kinetic energy is also zero.
3. Calculate the total energy:
Total Energy = Potential Energy + Kinetic Energy
Since the kinetic energy is zero, the total energy is equal to the potential energy.
Total Energy = 0.0392 J
Therefore, the total energy of the oscillation of the simple pendulum is 0.0392 Joules.
To calculate the total energy of the oscillation of a simple pendulum, you need to consider both the gravitational potential energy and the kinetic energy.
The gravitational potential energy (PE) is given by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height. In this case, m = 0.040 kg and h = 0.10 m. So the gravitational potential energy can be calculated as:
PE = (0.040 kg) * (9.8 m/s^2) * (0.10 m)
PE = 0.0392 Joules
The kinetic energy (KE) is given by the formula KE = (1/2) * m * v^2, where v is the velocity. For a pendulum, at the maximum height, the velocity is zero. Therefore, the kinetic energy is zero.
Since at the maximum height, the kinetic energy is zero, the total energy of the oscillation is equal to the gravitational potential energy.
Therefore, the total energy of the oscillation is 0.0392 Joules.