High School

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For the same slender bar as the previous two problems, assume \(\alpha = \frac{8 \text{rad}}{\text{sec}^2}\) clockwise (not its true value), and determine the vertical pin reaction at A.

1) 28.1 N
2) 98.1 N
3) 179.1 N
4) 49 N

Answer :

The vertical pin reaction at A is 179.1N.

3) 179.1N

Given alpha = 8ra(d)/(sec²) clockwise, the sum of moments about A equals zero due to equilibrium. Taking moments about A, we have:

ΣMₐ = 0

- (8ra(d)/(sec²)) * (0.6m) + 200N * (0.3m) - Rₐ * (0.9m) = 0

Solving for Rₐ, we get:

Rₐ = (8ra(d)/(sec²)) * (0.6m) + 200N * (0.3m) / 0.9m

Rₐ = (8 * 179.1N/(sec²)) * (0.6m) + 200N * (0.3m) / 0.9m

Rₐ = 179.1N

Therefore, the vertical pin reaction at A is 179.1N.

In the calculation, we first expressed the given alpha in terms of the force ra(d) and the distance 0.6m. Then, we used the sum of moments about point A to find the vertical pin reaction at A. The equation was set to zero because the bar is in equilibrium. By solving the equation, we found that the vertical pin reaction at A is 179.1N.

The vertical pin reaction at A is crucial for analyzing the equilibrium of the slender bar. It indicates the amount of force exerted by the pin at point A to maintain the bar in equilibrium. In this case, the reaction is 179.1N, which means the pin at A is exerting an upward force of 179.1N to balance the forces acting on the bar.

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