A 4.00-m-long, 470 kg steel beam extends horizontally from the point where it has been bolted to the framework of a new building under construction. A 75.0 kg construction worker stands at the far end of the beam. For the steps and strategies involved in solving a similar problem, you may view a Video Tutor Solution. What is the magnitude of the torque about the point where the beam is bolted into place?

12164.4 Nm

Explanation:

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Given values are;

m1= 470 kg

x= 4m

m2= 75kg

Cm = center of mass

g= acceleration due to gravity= 9.82 m/s^2

The distance of centre of mass is x/2

Center of mass(1) = x/2

But x= 4 m

Then substitute, we have,

Center of mass(1) = 4/2 = 2m

We can find the total torque, through the summation of moments that comes from both the man and the beam.

τ = τ(1) + τ(2)

But

τ(1)= ( Center of m1 × m1 × g)= (2× 470× 9.81)

= 9221.4Nm

τ(2)= X * m2 * g = ( 4× 75 × 9.81)= 2943Nm

τ = τ(1) + τ(2)

= 9221.4Nm + 2943Nm

= 12164.4 Nm

Hence, the magnitude of the torque about the point where the beam is bolted into place is 12164.4 Nm

pe = weightxheight = 2000x1000=2,000,000joules

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