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:
La tensión es 85.3 N.
Explanation:
Cuando el objeto gira en dirección horizontal, la sumatoria de fuerzas se puede calcular usando la segunda ley de Newton:
Dado que el movimiento es horizontal, el peso (que está en el eje y) no contribuye en la sumatoria de fuerzas en el eje x. Por lo que la única fuerza actuando sobre el objeto en la dirección del movimiento es la tensión.
En donde:
m: es la masa del objeto = 200 g = 0.200 kg
: es la aceleración centrípeta
La aceleración centrípeta viene dada por:
En donde:
ω: es la velocidad angular del objeto = 3 rev/s
r: es el radio = 1.20 m
Entonces, la tensión es:
Por lo tanto, la tensión es 85.3 N.
Espero que te sea de utilidad!
Answer:
Compared to windshield the airbag exerts much lesser force
Explanation:
Impulse is defined as change in momentum of the object when it is acted upon by a force during interval of time
<em>Impulse = Impulsive force *time</em>
I = F*Δt
If the object should be bought to rest from certain velocity there should be change in momentum. If the duration in which the momentum is increased then there would be less force applied and hence less damage.
Airbags are used to reduce the force experience by the people when they are met with accident by extending the time required to stop the momentum.
During the collision, the passenger is carried towards the<em> windshield</em> and if they are stopped by collision with wind shield the force will be larger and more damage.But if they are hit with airbag then the force will be less due to increased time.
The change is momentum will be the same with or without momentum but its the time that decides the impact of force.By making it longer the force become less.
<em>Thus compared to the windshield the airbag exerts much lesser force.</em>
<em> </em>
Answer:
The kinetic energy of the particle will be 12U₀
Explanation:
Given that,
A particle is launched from point B with an initial velocity and reaches point A having gained U₀ joules of kinetic energy.
Constant force = 12F
According to question,
The kinetic energy is
....(I)
Constant force = 12F
A resistive force field is now set up ,
Resistive force is given by,
When the particle moves from point B to point A then,
We need to calculate the kinetic energy
Using formula for kinetic energy
Put the value of 
Now, from equation (I)
Hence, The kinetic energy of the particle will be 12U₀.
Distance covered is given as follows
1). 7 km North
2). 5 km North
3). 1 km East
Now total distance covered will be given as
Now in order to find the displacement we will show all with their directions
towards North
towards East
So total displacement is
so net displacement will be
so displacement is 12.04 km
