Question

T. T. 2 7. Two blocks, each with mass m, are hung from the ceiling of an elevator, as shown. The elevator has upward acceleration a, and the strings have negligible mass. (a) Find the tensions T1 and T2 in the upper and lower strings. (b) Which string would break first if a is made sufficiently large? (c) What would the tensions be if the cable supporting the elevator broke?

Answer 1

7.

Solution :

(a)

For the lower block :

Equilibrium of forces , T₂ - F_g = F_net

where F_g is the force due to gravity . ( F_g = mg)

Acceleration is upward .

So ,

T₂ - mg = ma

T₂ = m(g+a)

For upper block :

Equilibrium of forces ,

T₁ - T₂ - F_g = F_net

T₁ = T₂ + mg + ma

= mg+ ma + mg + ma

= 2mg + 2ma

= 2m(g+a)

Or T₁ = 2T₂

Hence , T₁ = 2m(g+a) = 2T₂

T₂ = m(g+a)

(b)

As we have obtained in the first part , Tension in the upper string (T₁) is the twice of the tension in lower string (T₂)

So if a is made sufficiently large , then upper string would break first.

(c)

If cable supporting the elevator breaks, then there would be a free fall motion in downward direction, a = -g

So , T₁ = 2m(g-g) = 0

T₂ = m(g-g)= 0

T₁ = T₂ = 0 N