You take the opportunity to stock up on snacks and head on y

You take the opportunity to stock up on snacks and head on your way. You wind along the road for quite some time before you nd a very dark site and pull of onto dirt road. About 100 meters up the road your passage is stopped by a metal gate. The gate consists of a single heavy bar stretching 6 meters across the road. It looks like schedule 5 stainless steel pipe, of all things, clocking in at about 7 kg/linear meter if you recall correctly. It is hinged on the left side allowing you to lift it upwards. You know from experience that you can lift about 20 kg without much effort. Where should you lift the gate to apply the proper torque to move the bar?

Solution

We have a single heavy bar of length 6 metres. This heavy bar, as mentioned, is same as 5 stainless steel pipe of linear mass density 7 kg/linear metre.

That would imply that the gate would have a mass of 6 x 7 x 5 = 210 Kg

Now, we need to lift the gate of mass 210 Kg hinged at one end with a force equivalent to the weight of 20 Kg and for that to happen we will have to balance the torque produced by the weight.

The weight of the gate will produce a net torque of 210 x 3g = 630g Newtons about the left end of the bar.

As we can only apply a force of 20g N, the maximum torque which we can produce would 120 g.

Therefore, the gate cannot be lifted irrespective of the position of the torque applied.