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
A is pulling the block straight down toward the center of the Earth, no matter what the slope of the plane may be. A is the force of gravity.
The directions of B and C both depend on the slope of the plane.
B is a force that's parallel to the plane, pulling the block UP the plane. B is the force of friction.
C is a force perpendicular to the plane, preventing the block from falling down through the plane. C is the normal force.
Answer:
speed = distance/time
Explanation:
speed = 150/30
speed =5m/s
you were running fast .....5m/s is a good speed
