In the Atwood machine shown below, m1 = 2.00 kg and m2 = 7.60 kg. The masses of
ID: 1528409 • Letter: I
Question
In the Atwood machine shown below, m1 = 2.00 kg and m2 = 7.60 kg. The masses of the pulley and string are negligible by comparison. The pulley turns without friction and the string does not stretch. The lighter object is released with a sharp push that sets it into motion at vi = 2.30 m/s downward.
(a) What is the magnitude of the acceleration of m1?
1 m/s2
(b) How far will m1 descend below its initial level?
2 m
(c) Find the velocity of m1 after 1.80 s.
Explanation / Answer
atwood's machine
for block1
T - m1g = m1a
T = m1g + m1a...........(1)
for block 2
m2g - T = m2a..........(2)
substituting 1 in 2
m2g - m1g - m1a = m2a
m2g - m1g = m1a + m2a
g*(m2-m1) = a*(m1+m2)
acceleration , a = (m2-m1)*g/(m1+m2)
(a)
acceleration a = (7.6-2)*9.8/(7.6+2) = 5.72 m/s^2
(b)
vf^2 - vi^2 = 2*a*y
0 - 2.3^2 = -2*5.72*y
y = 0.46 m
(c)
v = vi + a*t
v = -2.3 + (5.2*1.8)
magnitude = 7.06 m/s
direction = upwards