Conservation of Energy
Energy, like momentum, is conserved. This means that if we add up the total energy of a system it will always be the same value, unless something enters or leaves the system.
As the ball bounces energy transfers form kinetic to gravitational.
When is kinetic energy the highest?
When is gravitational energy the highest?
When is rotational energy the hightest?
How is the total energy decreasing? Isn't energy conserved?
We can build an equation that sets the total energy at one moment in time equal to the total energy at another moment in time.
$$E_{i} = E_{f}$$
\( E_{i} \) = total initial energy [J] scalar\( E_{f} \) = total final energy [J] scalar
\( v \) = velocity[m/s] vector
Example: A 0.43kg soccer ball starts at rest and rolls down a 30m tall hill. How fast will the ball be moving at the bottom of the hill?
solution
$$E_{i} = E_{f}$$ $$U_{i} + K_{i} = U_{f} + K_{f}$$ $$mgh + \frac{1}{2}mv^{2} = mgh +\frac{1}{2}mv^{2}$$mass is in every term. lets divide y m