ne more query related to mechanics???????

Question

a light rod rests horizontally on supports at its ends.the rod carries 2 equal point loads,one at a distance x from one end and the other at distance x from the other end.show that the magnitude of the vertical force acting on the rod at each of the supports is independent of x.
a light clothes rail of length 2.5 m rests horizontally on supports at its ends.the rail has 25 identical garments hanging on it,at points distant(10n-5) cm from one end ,for n=1,2,....,25.the total weight of the garments is 250 N .state the magnitude of the vertical force acting on d rod at each of the supports.the garments 5th nd 14th from one end are removed.find the magnitude of the vertical force now acting on the rod at each of the supports.

Answer 1

Lets give the length of the rod a distance of L, and the weight of each mass N, and the reaction force vertically as R.

You can use the sum of all forces equal zero. In the vertical, it is the sum of the forces vertically, no horizontal matters.
2*N=2*R, N=R
You can also look at torques.

Summing at either end:
0=x*N+(L-x)*N-R*L
or R*L=x*N+L*N-x*N
R=N
since the rod is mass-less and the point masses are equal weight and equidistant from each end

For the second question

Each garment weighs 10 N the torque(using cmN) from the one end is

10*(5+15+25+35+45…+245)-250*R=0
R=31250/250
R=125 N (makes sense given the symmetry of the problem)


Removing #5 and # 14 (I used Excel, so it was easy to mod the formula

R=29450/250

R=117.8 N

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