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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We can solve the problem by using the first law of thermodynamics:
where
is the change in internal energy of the system
is the heat absorbed by the system
is the work done by the system on the surrounding
In this problem, the work done by the system is
with a negative sign because the work is done by the surrounding on the system, while the heat absorbed is
with a negative sign as well because it is released by the system.
Therefore, by using the initial equation, we find
Answer:
(a) t = 1.14 s
(b) h = 0.82 m
(c) vf = 7.17 m/s
Explanation:
(b)
Considering the upward motion, we apply the third equation of motion:
where,
g = - 9.8 m/s² (-ve sign for upward motion)
h = max height reached = ?
vf = final speed = 0 m/s
vi = initial speed = 4 m/s
Therefore,
<u>h = 0.82 m</u>
Now, for the time in air during upward motion we use first equation of motion:
(c)
Now we will consider the downward motion and use the third equation of motion:
where,
h = total height = 0.82 m + 1.8 m = 2.62 m
vi = initial speed = 0 m/s
g = 9.8 m/s²
vf = final speed = ?
Therefore,
<u>vf = 7.17 m/s</u>
Now, for the time in air during downward motion we use the first equation of motion:
(a)
Total Time of Flight = t = t₁ + t₂
t = 0.41 s + 0.73 s
<u>t = 1.14 s</u>