Question

2. (11 points) Alex is conducting an experiment with carts on an air track. Cart 1 has a mass of 400 grams, cart 2 has a mass of 200 grams, and cart 3 has a mass of 100 grams. The initial velocity of cart 1 is 12 m/s towards the stationary carts. The carts have repelling magnets on their ends so the carts will undergo elastic collisions. a) What will be the final velocity of cart 1 immediately after its collision with cart 2? b) What will be the final velocity of cart 2 immediately after its collision with cart 17 c) What will be the final velocity of cart 3 after its collision with cart 2? d) What will be the final velocity of cart 2 immediately after its collision with cart 3?

Answer 1

i s It is given in question estion The man of carte mi = 400 gm , My = 200gm and m₂ = 100gm .. Now the inital velocities of carts U, = 12 m/s (Toward m2) U₂=0 Uz=0 4, mi 42-0 m2. 4₂ =0 mg Now cart my first collides with me For the elastatic collision between me and my 9 The velocity of cart 1 after collision with cart-2 By formula de hotel offering va (mi-ma) a1 + 2 m2 42 " mitma v ų 4, 70 m2 4,>'. 00 X 10 X 6X2 - = (400x16- 200 x103) (12) +200 x10*xox2 400 xjö?+ 200X163 200 x163x12 +0 - 600x103 - 2 x 12 ac It is the it means it will moues 19Scanded miths la to in its initial direction

5) The velocity of Cast-2 imidiately after its collision with cast-1 9 x 400 x10 * 13 , . V = (m2 - m.) 42+2m, 44 mitma = (200 xjö 3 400x163 )x0+2 x 400x1oʻx 12. 200 x153+ 400x163 = 0 + 400 x12x109, - Gooxi-3 4812 7 'It is tve it means it will moves toward this. Cost-3) V = 8 miss TI and it will collide Now Cart-2 will movies toward Cart-3 to cart-3. : Now for elastic collision between Gart-2 and cart-3 El ma m3 AT c) How the velocity - of cart-3 After its collision with cart-2, V2 = (m3 - M2) Uz + 2 mg Vz CS Scanned withmitma CamScanner

V (100X10-3 200X163) xo + 2 x200x173x8 (100 + 200) X163 0 + 400X10-3x8 300 x103 V = V = 32 mle V = 10.67 mls a ş It is the it means it will more J- 1 in the direction of its d) Now velocity of cort-2 imielieately after collision with my. o'a (m2_m3) & + 2 m3 4₂ matma - (200x163 100x173) x8 + 2x100x16 30 (200 +100) x1003 100x163x8+o - 300 x103 = molts 2 gt is the means it will moves in its direction as it wass before collision anored 2 : 167 m las am Seatter