Answer :
Answer:
72.936 Joule
Explanation:
Mechanical Energy = Potential Energy + Kinetic Energy
Kinetic Energy = (1/2) x m x V² = (1/2) x 1.8 x 4.8² = 20.736 J
Potential Energy = m x g x h = 1.8 x 10 x 2.9 = 52.2 J
Total Mechanical Energy = 20.736 + 52.2 = 72.936 Joule
The mechanical energy of the book dropped from the top of the football stadium is 71.89 Joules.
Given the data in the question;
- Mass of the book; [tex]m = 1.8kg[/tex]
- Speed; [tex]v = 4.8m/s[/tex]
- Height; [tex]h = 2.9m[/tex]
Mechanical energy; [tex]E_{mechanical} = \ ?[/tex]
Mechanical energy is energy due to the position or movement of a particle or object. It is expressed as;
[tex]E_{mechanical} = Kinetic\ energy + Potential\ energy\\\\E_{mechanical} = \frac{1}{2}mv^2 + mgh[/tex]
Where m is mass of object, v is velocity, h is height and g is acceleration due to gravity { On earth, acceleration due to gravity [tex]g = 9.8m/s^2[/tex] }
We substitute our values into the equation
[tex]E_{mechanical} = [\frac{1}{2}*1.8kg*(4.8m/s)^2] + [ 1.8kg * 9.8m/s^2 * 2.9m ]\\\\E_{mechanical} = 20.736kg.m^2/s^2 + 51.156kg.m^2/s^2\\\\E_{mechanical} = 71.89kg.m^2/s^2\\\\E_{mechanical} = 71.89 J[/tex]
Therefore, the mechanical energy of the book dropped from the top of the football stadium is 71.89 Joules.
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