The uniform 100-kg beam is freely hinged about its upper end A and is initially at rest in the vertical position with theta = 0.
Determine the initial angular acceleration of the beam and the magnitude of the force FA supported by the pin at A due to the application of the force P = 300 N on the attached cable.
1 answer:
Answer:
ac = 2.86 m / s²
Explanation:
Image can detail the system to determine the force in the FA to understand the system into the applicated force
m = 100 kg , L = 3 m
∑ F = 0 ⇒ Ay - 100 kg + P * cos (45) = 0
Ay = 768.86 N
∑ Mₐ = α * I ₐ
I ₐ = m * L² / 3 ⇒ I ₐ = 100 kg * 4² m / 3
Replacing
P * sin (45) * 3 = α * 100 kg * 4² m / 3
α = 1.193 rad / s²
ac = α *2 ⇒ ac = 1.193 rad / s² * 2
ac = 2.86 m / s²
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Answer:
xmax = 9.5cm
Explanation:
In this case, the trajectory described by the electron, when it enters in the region between the parallel plates, is a semi parabolic trajectory.
In order to find the horizontal distance traveled by the electron you first calculate the vertical acceleration of the electron.
You use the Newton second law and the electric force on the electron:
(1)
q: charge of the electron = 1.6*10^-19 C
m: mass of the electron = 9.1*10-31 kg
E: magnitude of the electric field = 4.0*10^2N/C
You solve the equation (1) for a:
Next, you use the following formula for the maximum horizontal distance reached by an object, with semi parabolic motion at a height of d:
(2)
Here, the height d is the distance between the plates d = 2.0cm = 0.02m
vo: initial velocity of the electron = 4.0*10^6m/s
You replace the values of the parameters in the equation (2):
The horizontal distance traveled by the electron is 9.5cm