The starting angle θθ of a pendulum does not affect its period for θ<<1θ<<1. At higher angles, however, the period TT increases with increasing θθ.
The relation between TT and θθ can be derived by solving the equation of motion of the simple pendulum (from F=ma)
−gsinθ=lθ¨−gainθ=lθ¨
For small angles, θ≪1,θ≪1, and hence sinθ≈θsinθ≈θ. Hence,
θ¨=−glθθ¨=−glθ
This second-order differential equation can be solved to get θ=θ0cos(ωt),ω=gl−−√θ=θ0cos(ωt),ω=gl. The period is thus T=2πω=2πlg−−√T=2πω=2πlg, which is independent of the starting angle θ0θ0.
For large angles, however, the above derivation is invalid. Without going into the derivation, the general expression of the period is T=2πlg−−√(1+θ2016+...)T=2πlg(1+θ0216+...). At large angles, the θ2016θ0216 term starts to grow big and cause
When heat is added to a substance, the molecules and atoms vibrate faster. As atoms vibrate faster, the space between atoms increase. The motion and spacing of the particles determines the state of matter of the substance. The end result of increased molecular motion is that the object expands and takes up more space.
Answer: Your answer is<u> 1.36.</u>
Hope this helps!
Answer:
The value is 
Explanation:
From the question we are told that
The mass of matter converted to energy on first test is 
The mass of matter converted to energy on second test 
Generally the amount of energy that was released by the explosion is mathematically represented as
=> ![E = 1.5 *10^{-3} * [ 3.0 *10^{8}]^2](https://tex.z-dn.net/?f=E%20%3D%20%201.5%20%2A10%5E%7B-3%7D%20%20%2A%20%5B%203.0%20%2A10%5E%7B8%7D%5D%5E2)
=>
