Question

26 The figure shows a practical, simple experiment for determin- ing 9 to high precision. Two steel balls are suspended from electro- magnets, and are released simultaneously when the electric current is shut off. They fall through unequal heights A. and A.2. A computer records the sounds through a microphone as first one ball and then the other strikes the floor. From this recording, we can accurately determine the quantity T defined as T = Ate - Aty, i.e.. the time lag between the first and second impacts. Note that since the balls do not make any sound when they are released, we have no way of measuring the individual times Ato and Ati. (a) Find an equation for g in terms of the measured quantities T, ΔΙ, and Δ.r2. (b) Check the units of your equation. (e) Check that your equation gives the correct result in the case where is very close to zero. However, is this case realistic? (d) What happens when Am = Arg? Discuss this both mathemat- ically and physically. Problem 26.

Question 26 has parts A through D

Answer 1

9.7 kinematic eqr for 1st ball 4k, = 0 +ų gat 4142 = 0+4gate li tii) -(1) b.) Now Subtract eah i fsom li 422 - %, = 1g (ot - At) unit al Lt hand side SA Llis unit am Eg Right hand side of RMS unit = m.s2 =m Since LH3 = RHS hence this equation is correct Now, if ski=0 then st, will be also zero DK-055 g (4t7 -0%) => 4x2 = {g4b Yes this case is realistic se hence will be also zero $20 dy gf 14 = 8kg then sti = Ate hence sur-Am = sky-An = 1 g (Ate - Ath) O = O both will travel some distance hence both will take some since time.