A 1 kh pendulum os pulled sideways so that it is raised a vertical distance of 2 m above it's resting point. Find the max. Speed the pendulum reaches after being vertical
To find the maximum speed the pendulum reaches after being vertical, we can use the concept of conservation of energy.
First, let's determine the potential energy of the pendulum at its highest point, when it is raised 2 m above its resting point. The potential energy of an object is given by the equation:
Potential Energy = mass * gravity * height
In this case, the pendulum has a mass of 1 kg, gravity is approximately 9.8 m/s^2, and the height is 2 m. So the potential energy at the highest point is:
Potential Energy = 1 kg * 9.8 m/s^2 * 2 m = 19.6 J
Now, at the highest point, the maximum potential energy is converted to maximum kinetic energy, according to the law of conservation of energy:
Potential Energy at highest point = Kinetic Energy at lowest point
So, the maximum kinetic energy of the pendulum is also 19.6 J.
The kinetic energy of an object is given by the equation:
Kinetic Energy = (1/2) * mass * velocity^2
We need to solve for velocity, so let's rearrange the equation:
velocity = sqrt((2 * Kinetic Energy) / mass)
Plugging in the values, we get:
velocity = sqrt((2 * 19.6 J) / 1 kg) = sqrt(39.2 m^2/s^2) ≈ 6.26 m/s
Therefore, the maximum speed the pendulum reaches after being vertical is approximately 6.26 m/s.