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Cerrena [4.2K]
3 years ago
11

Blocks A (mass 2.00 kg ) and B (mass 14.00 kg , to the right of A) move on a frictionless, horizontal surface. Initially, block

B is moving to the left at 0.500 m/s and block A is moving to the right at 2.00 m/s. The blocks are equipped with ideal spring bumpers. The collision is headon, so all motion before and after it is along a straight line. Let +x be the direction of the initial motion of A. Part A Find the maximum energy stored in the spring bumpers.
Physics
1 answer:
tia_tia [17]3 years ago
4 0

Answer:

7.72 Joules

Explanation:

Data:

mass of block A = 2.00 kg

mass of block B = 14.00 kg

velocity of block A = 2.00 m/s

velocity of block B = 0.500 m/s

The fundamental assumption is that there is elastic collision, therefore, the momentum and energy of the system are conserved.

Thus:

U_{spring max} = KE_{total} - KE_{cm}\\  KE_{total} = \frac{1}{2}(mv_{1} ^{2}  + mv_{2} ^{2} )\\  = 0.5 (3.00(2.00)^{2}+ 14.00 (0.500)^{2} \\ = 7.75 J

V_{cm}  = \frac{3(2)-14(0.5)}{3+14} \\              = -0.0588m/s

The kinetic energy is given by the following:

KE_{cm} = \frac{1}{2}(m_{A} + m_{B})(v_{cm})^{2}  \\              = \frac{1}{2}(3.00 + 14.00) (-0.0588)^{2}  \\              = 0.03 J\\

Therefore, the maximum energy is given by the following:

U_{max} = 7.75 - 0.03\\               = 7.72 J

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