Answer:
0.833 N
Explanation:
Formula for Kinetic Energy [tex] E_k = \frac{mv^2}{2}[/tex]
Formula for Potential Energy [tex] E_p = mgy [/tex]
First we need to find the vertical distance between the maximum-angle position and the pendulum lowest point:
Using the swinging point as the reference, the vertical distance from the maximum-angle (34 degree) position to the swinging point is:
[tex] L * cos(34^o) = 1.2cos(34^o) = 1.2*0.83 = 0.995 \approx 1 m [/tex]
At the lowest position, pendulum is at string length to the swinging point, which is 1.2 m. Therefore, the vertical distance between the maximum-angle position and the pendulum lowest point would be
y = 1.2 - 1 = 0.2 m.
As the pendulum is traveling from the maximum-angle position to the lowest point position, its potential energy would be converted to the kinetic energy.
By law of energy conservation:
[tex] E_k = E_p [/tex]
[tex] \frac{mv^2}{2} = mgy[/tex]
[tex] v^2 = 2gy [/tex]
[tex]v = \sqrt{2gy}[/tex]
Substitute [tex]g = 10 m/s^2 [/tex] and y = 0.2 m:
[tex]v = \sqrt{2 * 10 * 0.2} = \sqrt{4} = 2 m/s [/tex]
At lowest point, pendulum would generate centripetal tension force on the string:
[tex] F = m\frac{v^2}{L} [/tex]
We can substitute mass m = 0.25, rotation radius L = 1.2 m and v = 2 m/s:
[tex] F = 0.25\frac{2^2}{1.2} = 0.833 N[/tex]
