a light spring has a mass of 0.2kg suspended from its lower end. a second mass of 0.1kg is suspended from the first by a thread. the arragement is allowed to come into static equilibrium and then the thread is burned through. at this instant, what is the upward acceleration of the 0.2kg mass?(take g as 10ms^-2)
ans:5.0 ms^-2
phy (mechanics)
2010-12-25 4:20 am
回答 (2)
2010-12-25 4:41 am
✔ 最佳答案
Let T be the tension in the spring and T' be the tension in the thread.Consider the 0.1 kg mass,
T' = 0.1g N = 1 N
Consider the 0.2 kg mass,
T = T' + 0.2g = (1 + 2) N = 3 N
At the instant when the thread is burnt, T' becomes zero, hence using net-force = mass x acceleration,
T - 0.2g = 0.2a
where a is the acceleration of the 0.2 kg mass
i.e. 3 - 0.2 x 10 = 0.2a
a = 1/0.2 m/s2 = 5 m/s2
2010-12-25 4:38 am
Let k be the elastic constant of the spring, then when the static equilibrium is reached:
kx = 0.3g = 3 where x is the extension of the spring.
Therefore at that time the tension of the spring is 3N.
So at the moment when the thread is burned:
Upward force = 3 N
Downward force = 2 N (weight of the mass)
So net force is 1 N upward.
Thus acc. is 1/0.2 = 5 m/s2 upward.
kx = 0.3g = 3 where x is the extension of the spring.
Therefore at that time the tension of the spring is 3N.
So at the moment when the thread is burned:
Upward force = 3 N
Downward force = 2 N (weight of the mass)
So net force is 1 N upward.
Thus acc. is 1/0.2 = 5 m/s2 upward.
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