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
The acceleration and velocity of the plane is 78.57 m/s² and 157.14 m/s respectively
To calculate the acceleration of the plane, we use the formula below.
<h3>Formula:</h3>
- a = F/m..................... Equation 1
Where:
- a = Acceleration of the plane
- F = Force applied to the plane
- m = mass of the plane.
From the question,
Given:
Substitute these values into equation 1
- a = 550000/7000
- a = 78.57 m/s²
To calculate the velocity, we use the formula below.
- v = u+at............. Equation 2
Where:
- v = Final velocity
- u = initial velocity
- a = acceleration
- t = time.
From the question,
Given:
- u = 0 m/s
- a = 78.57 m/s
- t = 2.0 seconds
Substitute these values into equation 2
Hence, The acceleration and velocity of the plane is 78.57 m/s² and 157.14 m/s respectively.
Learn more about acceleration here: brainly.com/question/460763
Answer:
Explanation:
<em>The top 5 winners of NASA's design contest winner received amount of </em><em> </em>(Dollar One hundred thousand)<em>. </em>The respected amount was divided into 5 parts as there were 5 winners as well.
So, the amount was divided among the winners are as follows:
<em>Winner 1 ⇒ </em>
<em>Winner 2 ⇒ </em>
<em>Winner 3 ⇒ </em>
<em>Winner 4 ⇒ </em>
<em>Winner 5 ⇒</em> 
Hence by adding all of the 5, we will get the answer, which is .
The momentum of any object is (the object's mass) times (its speed).
