Calculating Tension in Lower and Upper Wires with Mass and Acceleration

Question:

Two blocks of mass 2.9 kg and 1.9 kg are susended from a rigid support by two inextensible wires of each length 1 m . The lower wire has a uniform mass of 0.2 Kg per meter and the upper wire has a negligible mass.An upward acceleration of 0.2 ms^-2 is produced by the whole system (blocks,wires and support). Find the

• tension at the midpoint of the lower wire.
• tension at the midpoint of the upper wire.

Solution: Tension in lower and upper wires

Define the variables:

Let the upper block be of mass m1 =2.9 Kg

Lower block be of mass m2 = 1.9 Kg

Length of each wire = 1 m

Mass per unit length of the lower wire =0.2 Kgm^-1

Mass of the lower half-string= 0.1 Kg

Acceleration of the system (a) = 0.2 ms^-2

Gravitational acceleration (g) = 9.8 ms^-2

For the lower block:

Tension at the midpoint of the lower wire(T₁):

$${T_1- 2g = ma}$$

$${T_1-2(9.8)= 2(0.2)}$$

$${T_1 =0.4 + 19.6}$$

$${T_1= 20 \ N}$$

Tension at the midpoint of the lower wire = 20 N

Tension at the midpoint of the upper wire (T₂):

$${T_2- 5g=ma}$$

$${T_2-5(9.8)=5(0.2)}$$

$${T-2=1+49}$$

$${T_2=50 \ N}$$

Therefore the tension at the midpoint of the upper wire is 50 N

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