To solve this problem, we can apply Newton's second law of motion to both blocks individually.
For the 2 kg block:
The only force acting on the 2 kg block is the tension force from the string. According to Newton's second law, we have:
\(F = ma\)
where F is the net force on the block, m is the mass of the block, and a is the acceleration of the block.
The tension force T is pulling the block to the right, so we have:
\(F = T\)
Plugging this into the equation gives us:
\(T = ma\) ----(1)
For the 4 kg block:
The only force acting on the 4 kg block is the gravitational force. The gravitational force equals the mass of the block times the acceleration due to gravity (9.8 m/s²):
\(F = mg\)
where F is the net force on the block, m is the mass of the block, and g is the acceleration due to gravity.
The tension force T is also acting on the 4 kg block, but in the opposite direction to the gravitational force. This gives us:
\(F = mg - T\)
Plugging this into the equation with the tension force from equation (1), we get:
\(mg - T = ma\)
Substituting the values of 4 kg for m, 9.8 m/s² for g, and T from equation (1), gives us:
\(4(9.8) - T = 4a\) ----(2)
Now we have a system of two equations (equations (1) and (2)) with two unknowns (a and T). We can solve these equations simultaneously.
From equation (1):
\(T = 2a\) ----(3)
Substituting equation (3) into equation (2), we have:
\(4(9.8) - 2a = 4a\)
Simplifying and solving for a, we get:
\(39.2 = 6a\)
\(a = 39.2/6\)
\(a = 6.533\) m/s²
Therefore, the acceleration of the system is \(6.533\) m/s².
Substituting the value of a into equation (3), we can find the tension in the string:
\(T = 2(6.533)\)
\(T = 13.066\) N
Therefore, the tension in the string is \(13.066\) N.
Consider a block of mass 2 kg connected to a freely hanging block of mass 4 kg by a light and inextensible string which passes over a light pulley at the edge of a table. The 2 kg mass is on the surface of the table which is assumed to be smooth. Calculate the acceleration of the system and the tension in the string
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