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Given:
The mass of the pendulum bob, m=0.27 kg
The length of the string, L=1.5 m
The angle made by the string, θ=37°
To find:
The change in the gravitational potential energy.
Explanation:
The gravitational potential energy of an object is the energy possessed by the object due to the height at which the object is situated. The change in the gravitational potential energy of the pendulum will be directly proportional to the change in its height.
Where Δh is the change in the height of the bob, l is the vertical height of the string when it is at point A.
From the diagram,
[tex]l=L\cos \theta[/tex]And thus,
[tex]\begin{gathered} \Delta h=L-l \\ =L-L\cos \theta \\ =L(1-\cos \theta) \end{gathered}[/tex]The change in the gravitational potential energy of the object is given by,
[tex]\begin{gathered} \Delta E=mg\Delta h \\ =\text{mgL}(1-\cos \theta) \end{gathered}[/tex]Where g is the acceleration due to gravity.
On substituting the known values in the above equation,
[tex]\begin{gathered} \Delta E=0.27\times9.8\times1.5(1-\cos 37\degree) \\ =0.8\text{ J} \end{gathered}[/tex]Final answer:
Thus the change in the gravitational potential energy of the pendulum is 0.8 J
