1 20 pts In reviewing the concept of the block and tackle yo

1. (20 pts) In reviewing the concept of the block and tackle you devise a system as shown in the diagram below (assume all values are known to 3 significant digits). Both blocks start from rest. The surface is smooth, the cord is massless, and the pulleys are massless and frictionless a. What is the acceleration of each block? b. What is the tension in the cable? 10 30°

Solution

if acc. of block B is a then acc. of block A will be 3a.

and suppose tension in cable is T.

on block A: (applying Fnet = ma along the incline)

10gsin30 - T = 10(3a) = 30a    ........(i)

on block B:

3T - 8g = 8a

T - 8g/3 = 8a/3 ...... (ii)

adding equation (i) and (ii),

5g - 8g/3 = (8a/3 + 30a)

a = 0.7 m/s^2

(A) acceleration of block B is 0.7m/s^2 upward.

and acc. of block A is 3x0.7 = 2.1 m/s^2 downward.

(B) T - 8g/3 = 8a/3

T =8 (a + g)/3 = 8 (0.7 + 9.8) / 3

T = 28 N