Answer to Question #283128 in Physics for besr

Question

A physical therapist gone wild has constructed the (station- ary) assembly of massless pulleys and cords seen in Fig. 12-24. One long cord wraps around all the pulleys, and shorter cords suspend pulleys from the ceiling or weights from the pulleys. Except for one, the weights (in newtons) are indicated. (a) What is that last weight? (Hint: When a cord loops halfway around a pulley as here, it pulls on the pulley with a net force that is twice the tension in the cord.) (b) What is the tension in the short cord labeled T?

Answer 1

(a) the condition for equilibrium in the three left and last cords is

$$20+15+23=5+34+x,\\ x=19\text{ kg}.$$

(b) The tension is

$$T=9.8(19/2+5+34/2)=309\text{ N}.$$