Answer:
The ball has 7.35 joules of energy at position B.
The velocity of the ball at position A is 3.13 meter/second
Explanation:
Kinetic and Gravitational Potential Energy
Kinetic energy is the form of energy that an object or a particle has by reason of its motion. An object of mass m and speed v has kinetic energy calculated by:
[tex]\displaystyle K=\frac{1}{2}m.v^2[/tex]
Gravitational Potential Energy is the form of energy that an object has by reason of its height h relative to a certain reference. It can be calculated as follows:
[tex]U=m.g.h[/tex]
Where g is the acceleration of gravity.
The figure shows a pendulum with a bob (ball) of mass m=1.5 Kg. When it's pulled to point B, it has a height of h= 0.5 m and set to rest.
The potential energy at that point is:
[tex]U=1.5\ Kg\cdot 9.8 \ m/s^2\cdot 0.5\ m[/tex]
[tex]U=7.35\ J[/tex]
The ball has 7.35 joules of energy at position B.
When the ball is released, all of the potential energy is transformed into kinetic energy when reaches point A. Thus:
K=7.35 J
From the equation of kinetic energy, we solve for v:
[tex]\displaystyle v=\sqrt{\frac{2K}{m}}[/tex]
[tex]\displaystyle v=\sqrt{\frac{2\cdot 7.35}{1.5}}[/tex]
[tex]\displaystyle v=\sqrt{\frac{14.7}{1.5}}[/tex]
[tex]\displaystyle v=\sqrt{9.8}[/tex]
v = 3.13 m/s
The velocity of the ball at position A is 3.13 meter/second
