Answer:
The maximum height of the pendulum's swing is 0.32 m
Explanation:
The Principle Of Conservation Of Mechanical Energy
In the absence of friction, the total mechanical energy is conserved. That means that
Em=U+K is constant, being U the potential energy and K the kinetic energy
U=mgh
[tex]\displaystyle K=\frac{mv^2}{2}[/tex]
At the bottom of the swing, the pendulum has zero potential energy but its kinetic energy is at maximum. At the top of the swing, the pendulum has zero kinetic energy and the potential energy is at maximum.
Thus, applying the principle of conservation of mechanical energy:
[tex]\displaystyle mgh = \frac{mv^2}{2}[/tex]
Simplifying by m:
[tex]\displaystyle gh = \frac{v^2}{2}[/tex]
Solving for h:
[tex]\displaystyle h = \frac{v^2}{2g}[/tex]
Substituting:
[tex]\displaystyle h = \frac{2.5^2}{2*9.8}[/tex]
h = 0.32 m
The maximum heigth of the pendulum's swing is 0.32 m
