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:
The extension is directly proportional to the force applied.
ex: if the force is doubled, the extension doubles. This works until the limit of proportionality is exceeded.
Hope this helped~
Explanation:
Answer: The increase in temperature of the nail after the three blows is 8.0636 Kelvins. The correct option is (d).
Explanation:
Kinetic energy of the hammer ,K.E.=
Half of the kinetic energy of the hammer is transformed into heat in the nail.
Energy transferred to the nail in one blow =
Total energy transferred after 3 blows,Q =
Mass of the nail = 15 g = 0.015 kg
Change in temperature =
Specif heat of the steel = c = 448 J/kg K
The increase in temperature of the nail after the three blows is 8.1 Kelvins.Hence, correct option is (d).
Answer:
The force applied to make the object move
Answer:
B.
Explanation:
This is not true as the number of chromosomes in the daughter cells are half the number in the parent's cells
