Answer to Question #147671 in Mechanics | Relativity for Xavier

Question

1. A uniform rod of length 8 m and weight 50 N rests on a support that is 2m from A. The rod is held in a horizontal position by a force F that acts vertically downwards at A. a.Work out the magnitude of F. b.Work out the reaction at the support. 2. A uniform rod of length 7 m and weight 100N rests horizontally on two supports. Work out the values of the reactions R1, and R2, acting at the supports. 3. A uniform rod AB of mass Mkg and length Im, is held horizontally in equilibrium by two vertical strings attached at points A and C where AC:CB= 3:1. Find, in terms of m, the tensions T, and T, in the strings attached to the rod at A and C respectively. 4. A uniform rod AB, of weight 30N and length 6m, sits horizontally in equilibrium on two supports at points C And D as shown in the diagram. The reactions of the supports on the rod at points C and D are Rc and Rd, respectively. Given that Rc = 4Rd, work out the length x.

Answer 1

1) we have given the length of rod and it`s weight:

L=8m, P=50N, P means weight and P=m$\times$g ---> g=9.81 N/kg.

Let`s to find the magnitude of F:

in this case, moments will be equal:

M₁=M₂ --> F$\times$2=P$\times$2 --> F=P=50N.

Then we can find reaction force at supporter:

N(reaction force)=F+P=100N

2) we have given length and weight of rod:

L=7m, P=100N=m$\times$g.

There is a bit confusing of problem that the location of supporters did not given. But i will solve this problem by considering locations of supportes at the edges.

R₁$\times$L=P$\times$$\frac{L}{2}$ -->R₁=50N, then:

R₁+R₂=P --> R₂=P-R₁=50N.

Both of reaction forces are 50N

3) We have given mass and length of rod:

m=Mkg, L=lm, AC:CB=3:1.

T--> tensions on the strings

T_A$\times$3$\times$$\frac{I}{4}$=M$\times$g$\times$$\frac{I}{4}$ --> T_A=M$\times$$\frac{g}{3}$

T_c$\times$3$\times$$\frac{I}{4}$=M$\times$g$\times$2$\times$$\frac{I}{4}$ --> T_c=2$\times$M$\times$$\frac{g}{3}$

T_A and T_C are tensions on the strings.

4) Solving this problem is imposible without diagram. In the problem, diagram mentioned but not indicated.