Answer to Question #147673 in Mechanics | Relativity for Alina

Question

8 A plank AB has mass 10kg and length 6m. It is held in equilibrium in a horizontal position by two ropes attached at the points C and D, where AC= 1 m and DB = 2m. The plank can be modelled as a uniform rod and the ropes as light strings. a Work out: i the tension in the rope at C ii the tension in the rope at D. A mass of 5kg is placed on the plank at a distance xm from C, between Cand D. The mass can be modelled as a particle. Given that the plank remains in equilibrium in the horizontal position, b find, in terms of x, an expression for the tension in the rope at D. The rope at D will break if the tension exceeds 10g N. The rope at C cannot break. e Work out the range of possible values of x.

Answer 1

a) We have can calculate tensions at C and D pionts:

T_c$\times$ 3m=M$\times$g$\times$1m, T_c=$\frac{M\times g}{3}$=33.33N

2m$\times$M$\times$g=3m$\times$T_D--->T_D=2$\times$$\frac{M\times g}{3}$=66.66N

b) We can find expression:

x$\times$5$\times$g+2$\times$6$\times$g=3$\times$T -->T=$\frac{50\times x+120}{3}$ this is answer.