Blocks A (mass 7.00 kg ) and B (mass 15.00 kg ) move on a frictionless, horizont

Question

Blocks A (mass 7.00 kg ) and B (mass 15.00 kg ) move on a frictionless, horizontal surface. Initially, block B is at rest and block A is moving toward it at 1.00 m/s . The blocks are equipped with ideal spring bumpers. The collision is head-on, so all motion before and after the collision is along a straight line. Let +x be the direction of the initial motion of A.

A) Find the maximum energy stored in the spring bumpers and the velocity of each block at that time. Then Find the maximum energy.

B) Find the velocity of A.

C) Find the velocity of B.

D) Find the velocity of each block after they have moved apart. Find the velocity of A.

E) Find the velocity of B.

Explanation / Answer

A)

using conservation of momentum

mA VAi + mA VBi = (mA + mB) V

7 x 1 + 15 x 0 = (7 + 15) V

V = 0.32 m/s

E = energy stored in bumpers

using conservation of energy

(0.5) mA V2Ai + (0.5) mA V2Bi = (0.5) (mA + mB) V2 + E

0.5 x 7 x 12 + 0.5 x 15 x 02 = (0.5) (7 + 15) (0.32)2 + E

E = 2.4 J

b)

Velocity of A = V = 0.32 m/s

c)

Velocity of B = V = 0.32 m/s

d)

using conservation of momentum

mA VAi + mA VBi = mA VAf + mA VBf

7 x 1 + 15 x 0 =7 VAf + 15 VBf                

VAf = (7 - 15 VBf ) /7                   eq-1

Using conservation of KE

mA V2Ai + mA V2Bi = mA V2Af + mA V2Bf

7 x 12 + 15 x 0 =7 V2Af + 15 V2Bf   

7 = 7 ((7 - 15 VBf ) /7)2 + 15 V2Bf

VBf = 0.64 m/s

VAf = (7 - 15 VBf ) /7 = (7 - 15 (0.64) ) /7 = - 0.37 m/s

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