Find tension, aceleration and distance?

Question

Find tension, aceleration and distance?
Two objects with masses of 1.00 kg and 6.00 kg are connected by a light string that passes over a frictionless pulley as in Figure P4.34.

Figure P4.34: http://i165.photobucket.com/albums/u78/RLB31384/p4_34alt.gif

(a) Determine the tension in the string.
N
(b) Determine the acceleration of each object.
m/s2
(c) Determine the distance each object will move in the first second of motion if both objects start from rest.
m

Answer 1

Make a free body diagram

The forces acting on the 1 kg mass are the tension T and gravity

The forces acting on the 6 kg mass are the tension T and gravity.

Weight of 1 kg object = 9.8 N
Weight of 6 kg object = 58.8 N

The acceleration of the entire system we will call a.

T - 9.8 = 7a
58.8 - T = 7a

Subtract these two equations

2T - 49 = 0

T = 24.5 N

7a = 24.5 - 9.8
7a = 14.7

a = 2.1

Distance = 0.5 a t^2 = 0.5 (2.1) (1)^2 = 1.05 meters