Answer:
4.9 m/s²
Explanation:
Let T be the tension in the string
If a is the linear acceleration in the direction of the 3M mass, the equation of motion on the 3M mass is
3Mg - T = 3Ma (1)
Since the mass M moves upwards, its equation of motion is
T - Mg = Ma (2)
From (2)
T = Ma + Mg
substituting T into (1), we have
3Mg - (Ma + Mg) = 3Ma
3Mg - Ma - Mg = 3Ma
collecting like terms, we have
3Mg - Mg = 3Ma + Ma
2Mg = 4Ma
dividing both sides by 4M, we have
2Mg/4M = 4Ma/4M
g/2 = a
a = g/2
Since g = 9.8 m/s²,
a = 9.8 m/s²/2
a = 4.9 m/s²
The linear acceleration 'a' of the masses M and 3M is; a = 4.9 m/s²
We are told that;
Mass of first block = M
Mass of second block = 3M
Let the tension in the strings be T.
Now for first block we can write;
T - Mg = Ma - - - (1)
For second block, we can write;
3Mg - T = 3Ma - - - (2)
Where a is linear acceleration of the masses.
Let us add eq 1 to eq 2 to get;
T - Mg + 3Mg - T = Ma + 3Ma
2Mg = 4Ma
M will cancel out to get;
2g = 4a
Using division property of equality by dividing both sides by 2 to get;
g = 2a
Thus;
a = g/2
Where g is acceleration due to gravity = 9.8 m/s²
Thus;
a = 9.8/2
a = 4.9 m/s²
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