Help me find the solution to this physics problem?

Question

In the drawing the rope and the pulleys are mass less, and there is no friction. Find (a) the tension in the rope and (b) the acceleration of the 10.0-kg block.

image:http://i68.photobucket.com/albums/i38/jester21000/help.jpg

answer

(a) 13.7 N

(b) 1.37 m/s^2

Answer 1

Let:

T be the tension,

a be the acceleration of the 10kg block,

g be the acceleration due to gravity.

Then, as stated in the hint, the acceleration of the 3kg block is a / 2.

For the 10kg block:

T = 10a ...(1)

For the 3kg block:

3g - 2T = 3a / 2 ...(2)

(a)

Substituting for a from (1) in (2):

3g - 2T = 3T / 20

3g = 43T / 20

T = 60g / 43

= 13.7 N.

(b)

From (1):

a = T / 10

= 1.37 m/s^2.