Question

I need this type out answer question.

Answer 1

The ball has 7.35 joules of energy at position B.

The velocity of the ball at position A is 3.13 meter/second

Step-by-step 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:

`\displaystyle K=(1)/(2)m.v^2`

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:

`U=m.g.h`

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:

`U=1.5\ Kg\cdot 9.8 \ m/s^2\cdot 0.5\ m`

`U=7.35\ J`

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:

`\displaystyle v=\sqrt{(2K)/(m)}`

`\displaystyle v=\sqrt{(2\cdot 7.35)/(1.5)}`

`\displaystyle v=\sqrt{(14.7)/(1.5)}`

`\displaystyle v=√(9.8)`

v = 3.13 m/s

The velocity of the ball at position A is 3.13 meter/second