The direction of the acceleration ~a of the system is given in the figure. Three
ID: 1362832 • Letter: T
Question
The direction of the acceleration ~a of the system is given in the figure. Three masses (12 kg, 20 kg and 61 kg) are connected by strings. The 61 kg mass slides on a horizontal surface of a table top and the 12 kg and 20 kg masses hang over the edge of the surface. The string connecting the 12 kg and 61 kg masses runs over a massless and frictionless pulley. The coefficient of sliding friction, , between the 61 kg mass and the table top is 0 . 102. The acceleration of gravity is 9 . 8 m / s .
a)
Which equation represents
T
13
in the 12 kg
and 20 kg mass system?
b)
Which equation represents
T13the 61 kg
mass system?
Find the magnitude of acceleration of the sys-
tem.
Answer in units of m
/
s
2
.
Find the magnitude of acceleration of the sys-
tem.
Answer in units of m
/
s
2
.
Explanation / Answer
given,
mass A = 61 kg
mass B = 12 kg
mass C = 20 kg
coefficient of friction = 0.102
tension between 61 kg and 12 kg block T1
force equation of 61 kg block
T1 - 0.102 * 61 * 9.8 = 61 * a
force equation of 12 + 20 kg block
(12 + 20) * 9.8 - T1 = (12 + 20) * a
tension between 61 kg block and 12 kg block T1 = 226.675 N
acceleration of the system a = 2.716 m/s^2
force equation of 20 kg block
20 * 9.8 - T2 = 20 * 2.716
tension between 20 kg block and 12 kg block T2 = 141.68 N