Example of law of motion | Learn Physics

 Example of law of motion

Example of law of motion. Two loads masses m₁ and m₂ having a total mass 30 kg are suspended from a spring balance attached to ceiling of a lift moving upwards with an acceleration of 0.1 g. Determine the reading on the spring balance. Take g = 10 ms^-2 .

Solution: If the lift is stationary, and m₂> m₁, then load m₂ will fall down with acceleration say a₁ and load m₁ will rise up with acceleration a₁. If the lift is accelerated upwards with an acceleration a (=0.1 g) and T is the tension in the string, then for the motion of load m₁ , we have

T – m₁g = m₁(a + a₁) …………………………(i)

for the motion of load m₂ , we have

T – m₂g = m₂(a - a₁) …………………………(ii)

Adding (i) and (ii), we get

2T – (m₁+m₂)g = (m₁+m₂)a+(m₁-m₂)a₁

Or       2T =(m₁+m₂)(g +a)-- (m₁-m₂) a₁                                           

Ignoring the second term, being too small,

Reading on spring balance = 2T = (m₁+m₂)(g +a)

=30(9.8 + 0.98)= 30  × 10.78 N

=30  × 10.78/9.8 = 33 kg wt.