## he uniform 110-kg beam is freely hinged about its upper end A and is initially at rest in the vertical position withθ= 0. Determine the init

Question

he uniform 110-kg beam is freely hinged about its upper end A and is initially at rest in the vertical position withθ= 0. Determine the initial angular accelerationα of the beam and the magnitudeFAof the force supported by the pin at A due to the application of the force P = 350 N on the attached cab

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2 months 2021-07-31T07:08:39+00:00 2 Answers 1 views 0

The initial angular acceleration of the beam is

The magnitude of the force at A is 832.56N

Explanation:

Here, m is the mass of the beam and l is the length of the beam.

Take the moment about point A by applying moment equilibrium equation.

Here, P is the force applied to the attached cable and is the angular acceleration.

Substitute 350 for P and 586.67kg.m² for I

The initial angular acceleration of the beam is

Find the acceleration along x direction

Here, r is the distance from center of mass of the beam to the pin joint A.

Substitute 2 m for r and 1.3056rad/s² for

Find the acceleration along the y direction.

Here, ω is angular velocity.

Since beam is initially at rest,ω=0

Substitute 0 for ω

Apply force equilibrium equation along the horizontal direction.

Apply force equilibrium equation along the vertical direction.

Calculate the resultant force,

The magnitude of the force at A is 832.56N

a) Initial angular acceleration of the beam = 1.27 rad/s²

b)

Explanation:

Force applied to the attached cable, P = 350 N

Mass of the beam, m = 110-kg

Mass moment of the inertia of the beam about point A =

Using the parallel axis theorem

Moment = Force * Perpendicular distance

From the free body diagram drawn

P = 350 N, l = 3+ 1 = 4 m, θ = 45°

Substitute these values into the equation above

Linear acceleration along the x direction is given by the formula

r = 2 m

the linear acceleration along the y-direction is given by the formula

Since the beam is initially at rest, w = 0

General equation of motion along x – direction

General equation of motion along y – direction

Magnitude of the force supported by the pin at A