Question

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.

Answer 1

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:

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