A box of mass m 2 = 3.7 kg rests on a frictionless horizontal shelf and is attac
ID: 1277102 • Letter: A
Question
A box of mass m2 = 3.7 kg rests on a frictionless horizontal shelf and is attached by strings to boxes of masses m1 = 1.7 kg and m3 = 2.5 kg as shown below. Both pulleys are frictionless and massless. The system is released from rest. After it is released, find the following.
1)
(a) the acceleration of each of the boxes a1 = m/s2
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2)
a2 = m/s2
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3)
a3 = m/s2
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4)
(b) the tension in each string T1 = N
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5)
T2 = N
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Explanation / Answer
The forces on m1...
T1 - mg = ma
T1 - 1.7(9.8) = 1.7a
T1 = 1.7a + 16.66
The forces on m3
mg - T2 = ma
2.5(9.8) - T2 = 2.5a
T2 = 24.5 - 2.5a
The forces on m2
T2 - T1 = ma
T2 - T1 = 3.7a
Sub in the T2 and the T1 from above
24.5 - 2.5a - 1.7a - 16.66 = 3.7a
7.84 = 7.9a
a = .992 m/s2
The accelerations will all be the same magnitude for all of the boxes (Thus parts 1, 2, and 3 will be the same answer)
However, a1 is upward at .992 m/s2, a2 is to the right at .992 m/s2 and a3 is downward at .992 m/s2 (so your key may want a negative for that since its downward)
Part 4)
T1 = 1.7(.992) + 16.66
T1 = 18.3 N
Part 5)
T2 = 24.5 - 2.5(.992)
T2 = 22.0 N
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