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
Answer:
6.51 g/c.c
Explanation:
mass, m = 114 g
initial volume, V1 = 25 mL
final volume, V2 = 42.5 mL
Volume of the metal piece, V = V2 - V1 = 42.5 - 25 = 17.5 mL
1 mL = 1 c.c
So, Volume of metal, V = 17.5 c.c.
Let the density of the metal is d.
density = mass / volume
d = 114 / 17.5 = 6.51 g/c.c
Thus, the density of metal is 6.51 g/c.c.
Mixing something into a liquid to create a solution.
Chemistry for Biologists: Some basic chemistry
Some basic chemistry
Living organisms and chemistry
Biology is about living things - organisms. All living organisms are made of chemicals. To understand biological substances and the changes that take place in living organisms you need a good knowledge of the underlying chemistry. We will build up a picture of the chemicals that make up living organisms by starting small and getting bigger.
The starting point is atoms - the building blocks of all matter. We will then look at how these come together to make elements and compounds.
