a) The speed of the bead at B is 11.79m/s.
b) The change in mechanical energy due to friction as it moves from B to C is 36.064 J.
If we drop the object from the shelf or release the spring, that potential energy is converted back into kinetic energy. Kinetic energy can also be transferred from one body to another in a collision, which can be elastic or inelastic.
a)
Potential energy is converted to kinetic energy
[tex]\frac{1}{2} mv^2=mgh\\\\v=\sqrt{2gh} \\\\v_B=\sqrt{2(9.8)(7.1-0)} \\\\v_B=11.79m/s[/tex]
The speed of the bead at B is 11.79m/s.
b)
[tex]W = mg(h_A) - mg(h_B) = 0.8(9.8)(7.1 - 2.5) = 36.064 J\\\\W=36.064J[/tex]
The change in mechanical energy due to friction as it moves from B to C is 36.064 J.
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