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:
Einstein's equivalence principle says that __________.
the effects of gravity are exactly equivalent to the effects of acceleration
Explanation:
The equivalence principle is one of the fundamental laws of physics, as enunciated by Einstein. It categorically states that the gravitational and inertial forces are of a similar nature. In physics, a gravitational acceleration is the acceleration of an object in a free fall within a space. The importance of Einstein's Equivalence Principle is explained by his theory of general relativity. This theory states that mass is the same, whether inertial or gravitational.
Answer:
The pitch that he hears after the truck passes and is moving away is 819.6 Hz.
Explanation:
The pitch that he hears after the truck passes and is moving away can be calculated using the following equation:
Where:
: is the perceived frequency
: is the emitted frequency
: is the speed of sound = 340 m/s
: is the speed of the observer = 0 (he is not moving)
: is the speed of the fire truck
First, we need to find the speed of the fire truck. When it approaches the observer we have:
Hence, the speed of the fire truck is 25.05 m/s.
Now, we can calculate the pitch that the observer hears after the truck passes:
Therefore, the pitch that he hears after the truck passes and is moving away is 819.6 Hz.
I hope it helps you!
<span>C. As a metal comb is held near an object with a negative charge, the comb becomes charged.
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