The motor draws in the cable with an acceleration of3 ms2 Th

The motor draws in the cable with an acceleration of3 m/s2. The beam has a uniform mass of 30 kg/m , and the crate has a mass of 220 kg . Neglect the mass of the motor and pulleys. (Figure 1)

Part A

Determine the components of the reaction at the support A using scalar notation.

Express your answers using three significant figures separated by a comma.

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Part B

Determine the reaction at the support B.

Express your answer to three significant figures and include the appropriate units.

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Figure 1 of 1

Solution

It is evident from the figure that acceleration of the crate = 3/2 = 1.5 m/s2

So, 2T - mg = ma

So, T = m(a+g)/2 = 220*(1.5+9.8)/2 = 1243 N

Now, equating torques about A:

Fb*(2.5+0.5+3) = T*(2.5+0.5) + 30*6*9.8*(6/2)

So, Fb*(2.5+0.5+3) = 1243*(2.5+0.5) + 30*6*9.8*(6/2)

So, Fb = 1503.5 N = 1.504 kN = By <--------- answer for part B

Now, equating forces in horizontal : So, Ax = 0 <-------answer for part A

Equating forces in vertical:

Ay +By = T

So, Ay = T - By = 1243.2 - 1503.5

= -260 N

= 0.26 kN <------answer for part A