The mechanical energy is 71.9 J
Explanation:
The mechanical energy of an object is equal to the sum of its potential energy (PE) and its kinetic energy (KE):
E = PE + KE
Where:
The potential energy is given by
[tex]PE=mgh[/tex]
where
m is the mass of the object
g is the acceleration of gravity
h is the height above the ground
The kinetic energy is given by:
[tex]KE=\frac{1}{2}mv^2[/tex]
where
v is the speed of the object
Re-arranging the equation,
[tex]E=mgh+\frac{1}{2}mv^2[/tex]
For the book in this problem, we have:
m = 1.8 kg
v = 4.8 m/s
h = 2.9 m
And
[tex]g = 9.8 m/s^2[/tex]
Substituting, we find the mechanical energy:
[tex]E=(1.8)(9.8)(2.9)+\frac{1}{2}(1.8)(4.8)^2=71.9 J[/tex]
Learn more about kinetic and potential energy:
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