Physic Labs

Problem 1

A simple pendulum consists of a small bob of mass m=0.50m=0.50 kg on a light inextensible string of length L=1.25L=1.25 m attached to a fixed support. The string is displaced to one side until it makes 60∘60^\circ with the vertical and is released from rest. Neglect resistance and take g=10g=10 m/s2^2. (a) Find the bob's height above the lowest point just before release. (b) Find its speed through the lowest point. (c) Find the string tension there. (d) Find the angle to the vertical where kinetic energy equals potential energy above the lowest point.
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L(1−cos⁡θ)=h02=L4⇒cos⁡θ=34⇒θ=41.4∘L(1-\cos\theta)=\frac{h_0}{2}=\frac{L}{4}\Rightarrow \cos\theta=\frac34\Rightarrow \theta=41.4^\circ
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Substitute the geometric relation y=L(1−cos⁡θ)y=L(1-\cos\theta) and solve the energy condition. The angle is 41.4∘41.4^\circ; final results are h=0.625h=0.625 m, v0=3.54v_0=3.54 m/s, T=10T=10 N and θ=41.4∘\theta=41.4^\circ.