M1 tough moments questionWatch
A large log AB is 6 m long. It rests in a horizontal position on two smooth supports C and D, where AC = 1 m and BD = 1 m, as shown in Figure 4. David needs an estimate of the weight of the log, but the log is too heavy to lift off both supports. When David applies a force of magnitude 1500 N vertically upwards to the log at A, the log is about to tilt about D.
(a) State the value of the reaction on the log at C for this case.
David initially models the log as uniform rod. Using this model,
(b) estimate the weight of the log
The shape of the log convinces David that his initial modelling assumption is too simple. He removes the force at A and applies a force acting vertically upwards at B. He finds that the log is about to tilt about C when this force has magnitude 1000 N. David now models the log as a non-uniform rod, with the distance of the centre of mass of the log from C as x metres. Using this model, find
(c) a new estimate for the weight of the log,
(d) the value of x.
(e) State how you have used the modeling assumption that the log is a rod.
- Study Helper
Okay I can it all apart from (c) (I can do d with c). I really don't understand how the weight of the log can have changed..Surely it's the same log never mind if it's uniform etc...If anyone could talk me thorugh part c) it would be much appreciated, thanks!
However, making the assumption that the centre of gravity is in the middle of the log, an estimate of the weight of the log is worked out in part (b).
Then, David realises that the assumption wasn't a good one. So now we model the log as having its center of gravity/mass at an unknown position - "x" from C. And work out a new estimate for the weight, based on the additional information.