Answer with Explanation:
Mass of pendulum bob, m=0.453 kg
Speed, [tex]v_1=[/tex]2.58 m/s
a.r=75.1 cm=[tex]75.1\times 10^{-2}m[/tex]=0.751 m
[tex] 1cm=10^{-2} m[/tex]
Tension in the pendulum cable is given by
Tension=Centripetal force+force due to gravity
[tex]T=\frac{mv^2}{r}+mg[/tex]
Where [tex]g=9.8 m/s^2[/tex]
Substitute the values
[tex]T=\frac{0.453(2.58)^2}{75.1\times 10^{-2}}+0.453\times 9.8[/tex]
[tex]T=8.45 N[/tex]
b.When the pendulum reaches its highest point,then
Final velocity, [tex]v_2=0[/tex]
According to law of conservation of energy
[tex]mgh_1+\frac{1}{2}mv^2_1=mgh_2+\frac{1}{2}mv^2_2[/tex]
[tex]gh_1+\frac{1}{2}v^2_1=gh_2+\frac{1}{2}v^2_2[/tex]
[tex]h_1=0[/tex]
Substitute the values
[tex]9.8\times 0+\frac{1}{2}(2.58)^2=9.8\times h_2+\frac{1}{2}(0)^2[/tex]
[tex]3.3282=9.8h_2[/tex]
[tex]h_2=\frac{3.3282}{9.8}=0.34 m[/tex]
The angle mad by cable with the vertical=[tex]cos\theta=\frac{0.751-0.34}{0.751}=0.55[/tex]
[tex]\theta=cos^{-1}(0.55)=56.6^{\circ}[/tex]
c.When the pendulum reaches at highest point then
Acceleration, a=0
Therefore, the tension in the pendulum cable
[tex]T=mgcos\theta[/tex]
Substitute the values
[tex]T=0.453\times 9.8cos56.6[/tex]
[tex]T=2.4 N[/tex]
