Answer :
The magnitude of the reaction force at support A is calculated using the principles of static equilibrium. The reaction force RA is found to be 208.5 lb by balancing the moments around support B and applying the formula for moments (M = Force * distance).
To determine the magnitude of the reaction force at support A for a given system with a weight P positioned on a beam split into segments a and b, we need to apply the principles of static equilibrium. The system needs to satisfy two conditions: the sum of all the vertical forces must be zero (upward forces equal downward forces), and the sum of the moments around any pivot point must also be zero.
For this particular problem, the weight P acts downward at a distance (a+b) from support A. To keep the system in equilibrium, support A must provide an upward reaction force (let's call it RA). The sum of the moments around support B will then be zero if the moment caused by P is counterbalanced by the moment caused by RA. Using the formula M = Force * distance, we can solve for RA:
Moment about B due to P = P * (a+b)
Moment about B due to RA = RA * b
Since the system is in equilibrium, we have: RA * b = P * (a+b),
Solving for RA gives us:
RA = P * (a+b)/b
Plugging in the given values, we find:
RA = 139 lb * (4 ft + 8 ft) / 8 ft
RA = 139 lb * 12 ft / 8 ft
RA = 139 lb * 1.5
RA = 208.5 lb
The reaction force at support A is therefore 208.5 lb.
