CALC? To study damage to aircraft that collide with large birds, you design a test gun that will accelerate chicken-sized objects so that their displacement along the gun barrel is given by x = (9.0 X 103 m/s2)t2 – (8.0 X 104 m/s3)t3. The object leaves the end of the barrel at t = 0.025 s. (a) How long must the gun barrel be? (b) What will be the speed of the objects as they leave the end of the barrel? (c) What net force must be exerted on a 1.50-kg object at (i) t = 0 and (ii) t = 0.025 s?
Solution 45P Step 1: The displacement along the gun barrel (x) = (9.0x10 m/s )t (8.0x10 m/s )t 4 3 3 Time taken by the object to leave the barrel (t) = 0.025s Problem (a) Step 1: Length of the barrel = x(0.025) 3 2 4 3 = 9x10 * (0.025) 8x10 * (0.025) = 5.625-1.25 Length of the barrel = 4.375 m Problem (b) Step 1: Speed of the object = dx dt 3 4 2 v = 18x10 t 24x10 t Step 2: Time it takes to leave the barrel = 0.025s v = 18x10 (0.025) 24x10 ( 0.025 ) 2 v = 450-150 v = 300 m/s Problem (c) To find the net force on the object Step 1: dv Acceleration (a) = dt a = 18x10 48x10 t 4 Step 2: At t = 0s 3 4 a = 18x10 48x10 (0) 3 2 a = 18x10 m/s Step 3: At t = 0.025s 3 4 a = 18x10 48x10 (0.025) 3 a = 6x10 m/s 2