physics question #5?
A light, inextensible cord passes over a light,
frictionless pulley with a radius of 13 cm. It
has a(n) 23 kg mass on the left and a(n)
9.5 kg mass on the right, both hanging freely.
Initially their center of masses are a vertical
distance 3.7 m apart.
The acceleration of gravity is 9.8 m/s2. At what rate are the two masses accelerating when they pass each other?
Answer in units of m/s
- WhomeLv 74 weeks ago
F = ma
23(9.8) - 9.5(9.8) = (23 + 9.5)a
a = 9.8(23 - 9.5) / (23 + 9.5)
a = 0.4153...
a = 0.42 m/s² ANSWER
The 9.5 kg mass will accelerate at this rate upward, the 23 kg mass will accelerate downward.
If the question is actually at what velocity do they pass each other
The net acceleration is twice the above value and the distance is half of that reported.
v² = u² + 2as
v² = 0² + 2(2(0.4153))(3.7 / 2)
v² = 0² + 2(0.4153)(3.7)
v² = 3.0738
v = 1.7532...
v = 1.8 m/s
Answers have been rounded to the two significant digits of the question numerals.
I hope this helps.
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