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
Explanation:
we use the formula, Vf=Vi+at
since the cheetah accelerated from rest, it's initial speed is 0, 27=0+a (6.75), a=4 m/s2
C.
hope that helped you!!!
Answer:24
Explanation:
First you need to calculate the acceleration, for this use can use the following formula Force (F) = Mass (M) x Acceleration (A). If we extract A out of this, you can get the following equation A = F/M = 4/0.5 = 8 m/s^2. So, the object accelerates each second by 8 m/s, if the object does this for 3 second, the velocity would be 8 x 3 = 24
Which of the following is not a an example of dissipated energy?
b. kinetic
When energy is changed from one form to another, ____.
b. all of the energy can be accounted for