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Let [tex]P = 139 \text{ lb}[/tex], [tex]a = 4 \text{ ft}[/tex], and [tex]b = 8 \text{ ft}[/tex].

Determine the magnitude of the reaction force at support A.

(Note: Type the unit "lb" after typing your numerical answer.)

Answer :

The magnitude of the reaction force at support A is calculated using the moment due to force P applied at a distance a + b with a 30° angle. The reaction force at A creates an equal but opposite moment, and thus RA is found to be 208.5 lb.

To determine the magnitude of the reaction force at support A, we need to consider the system at equilibrium, meaning the sum of the moments about any point is zero. Since we have a force P applied at a distance of 'a + b' from support A and an angle of 30°; we will calculate the moment about point A.

The moment about point A due to force P is given by:

MA = P * (a + b) * sin(30°)

Plugging in the values, we get:

MA = 139 lb * (4 ft + 8 ft) * sin(30°) = 139 lb * 12 ft * 0.5

The moment about A is then MA = 834 lb*ft. Since the system is in equilibrium, the reaction force at A will create an equal but opposite moment.

Therefore, the magnitude of the reaction force at A is equal to 834 lb*ft divided by the lever arm 'a', which is 4 ft:

RA = MA / a

RA = 834 lb*ft / 4 ft

Therefore, the magnitude of the reaction force at support A is RA = 208.5 lb.

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