At the lowest point in its swing, a 2.5 kilogram pendulum bob has 40 Joules of kinetic energy. How high will its swing when it reaches the highest point in its swing?
The height H will satisfy the equation
M*g*H = 40.
H = 40/(2.5*9.8) meters
To determine how high the pendulum bob will swing at its highest point, we need to consider the principle of conservation of mechanical energy. At the highest point, all of the pendulum's kinetic energy will be converted into potential energy.
To calculate the potential energy at the highest point, we can equate it to the initial kinetic energy at the lowest point. The formula for potential energy is given by:
Potential Energy (PE) = mgh
Where:
m = mass of the pendulum bob = 2.5 kg
g = acceleration due to gravity = 9.8 m/s^2
h = height of the swing at the highest point (what we want to find)
By equating the potential energy and the initial kinetic energy, we have:
PE = KE
mgh = KE
Plugging in the given values:
2.5 kg * 9.8 m/s^2 * h = 40 J
Simplifying the equation:
h = 40 J / (2.5 kg * 9.8 m/s^2)
h ≈ 1.63 meters
Therefore, the pendulum bob will swing approximately 1.63 meters high at its highest point.