Respuesta :
Answer:
a) The angular acceleration of the beam is 0.5 rad/s²CW (direction clockwise due the tangential acceleration is positive)
b) The acceleration of point A is 3.25 m/s²
The acceleration of point E is 0.75 m/s²
Explanation:
a) The relative acceleration of B with respect to D is equal:
[tex]a_{B} =a_{D} +(a_{B/D} )_{n} +(a_{B/D} )_{t}[/tex]
Where
aB = absolute acceleration of point B = 2.5 j (m/s²)
aD = absolute acceleration of point D = 1.5 j (m/s²)
(aB/D)n = relative acceleration of point B respect to D (normal direction BD) = 0, no angular velocity of the beam
(aB/D)t = relative acceleration of point B respect to D (tangential direction BD)
[tex]a_{B} =a_{D} +(a_{B/D} )_{t}[/tex]
[tex]2.5j=1.5j +(a_{B/D} )_{t}\\(a_{B/D} )_{t}=j=1m/s^{2}[/tex]
We have that
(aB/D)t = BDα
Where α = acceleration of the beam
BDα = 1 m/s²
Where
BD = 2
[tex]2\alpha =1\\\alpha =0.5rad/s^{2}CW[/tex]
b) The acceleration of point A is:
[tex]a_{A} =a_{D} +(a_{A/D} )_{t}[/tex]
(aA/D)t = ADαj
[tex]a_{A} =a_{D} +AD\alpha j\\a_{A}=1.5j+(3.5*0.5)j\\a_{A}=3.25jm/s^{2}[/tex]
The acceleration of point E is:
(aE/D)t = -EDαj
[tex]a_{E} =a_{D} -ED\alpha j\\a_{E}=1.5j-(1.5*0.5)j\\a_{E}=0.75jm/s^{2}[/tex]
(a) The angular acceleration of the beam is 0.5 rad/s²
(b) The acceleration of points A and E is 3.25 rad/s² and 0.75 rad/s² respectively.
Angular acceleration:
Given that the length of the steel beam is L = 5m
the deceleration of the cable at B the instant is a(B) = 2.5 m/s²
the deceleration of the cable at D the instant is a(D) = 1.5 m/s²
(a) The relation between the acceleration of B and D is:
a(B) = a(D) + a(R)
where a(R) is the relative acceleration of B with respect to D
a(R) = a(B) - a(D)
a(R) = 2.5 - 1.5
a(R) = 1 m/s²
Let the angular acceleration be α, then:
a(R) = α×BD
BD = 2m, thus
α = a(R)/BD
α = 1/2 rad/s²
α = 0.5 rad/s²
(b) The acceleration of point A will be:
a(A) = a(D) + α×AD
a(A) = 1.5 + 0.5×3.5
a(A) = 3.25 rad/s²
The acceleration of point E will be:
a(E) = a(D) - α×ED
a(E) = 1.5 - 0.5×1.5
a(E) = 0.75 rad/s²
Learn more about angular acceleration:
https://brainly.com/question/26133378?referrer=searchResults
