From the diagram above, what is the: a) magnitude of the reaction force on the b
ID: 3278660 • Letter: F
Question
From the diagram above, what is the: a) magnitude of the reaction force on the beam at A? b) the direction of the reaction force on the beam at A?(angle CCW from X-axis) c) the magnitude of the reaction force on the beam at B? d) the direction of the reaction force on the beam at B? (angle CCW from X-axis)Note: there is a glitch on the right side in the picture; the measurement for the B beam is .8m at the tip and 1.1m below 6. 500 N 740N 65 Tet 1.7m 3.7 m Drawing not to scale. Neglect the weight of the beam. EXAMPLE NOTES IMAGES DISCUSS UNITS STATS HELP Part Description Answer Chk What is the magnitude of the reaction force on the beam at A? (include units with answer) 9.02 pts·110% A. Format Check 2% try penalty in What is the direction of the reaction force on the beam at A? (angle CCW from X axis) (include units with answer) 9.02 pts. 110% B. Format Check 2% try penalty Hints: 2.0 What is the magnitude of the reaction force on the beam at B? (Include units with answer) 9.02 pts., 10% # tri C. Format 2% try penalty
Explanation / Answer
let the reaction force at B be Rb, acting towards left and Nb acting in +y direction
let the reaction force at A be Ra, acting towards +y axis ( there is no horizontal component of reaction as this is a roller support)
so, From force balance along both the direction (+x and +y directions) we get
by using conditions for static equilibrium
500 - 740cos(65) = Rb
740*sin(65) = Ra + Nb
so, Rb = 187.262 N
now, from moment balance about point B
500*0.8 + Ra*3.7 = 740cos(65)*1.1 + 740*sin(65)(1.7+3.7)
Ra = 963.6803 N
Nb = -293.0125 N
so,
a. Ra = 963.6803 N
b. direction of Ra = 90 degree CCW from x axis
c. Reaction at B, R = sqroot(Rb^2 + Nb^2) = 347.74 N
d. direction of R = arctan(Nb/Rb) = 237.417 degree CCW of x axis
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