Have you ever listened for an approaching train by kneeling next to a railroad track and putting your ear to the rail? Young's modulus for steel is Y = 2.0 1011 N/m2, and the density of steel is rho = 7860 kg/m3. On a day when the temperature is 19° C, how many times greater is the speed of sound in the rail than in the air? (Treat air as an ideal gas of particles with mass 4.78 10-26 kg and with γ = 1.40.)

Visualize the problem and identify special cases first examine the problem by drawing a picture and visualizing the motion. apply newton's 2nd law, ∑f⃗ =ma⃗ , to each body in your mind. don't worry about which quantities are given. think about the forces on each body: how are these consistent with the direction of the acceleration for that body? can you think of any special cases that you can solve quickly now and use to test your understanding later? one special case in this problem is if m2=0, in which case block 1 would simply fall freely under the acceleration of gravity: a⃗ 1=−gj^.