Answer :
6.01 × 10⁻⁵ m/s is speed of 0.100 kg sphere when it has moved 0.400 m to right from its initial position.
What is conservation of energy?
The conservation of energy principle states that in a closed system, the energy of interacting objects or particles remains constant. Kinetic energy, sometimes known as the energy of motion, was the first type of energy to be identified. The sum of the kinetic energy of the particles before collision and the sum of the kinetic energy of the particles after collision are equal in some particle collisions, known as elastic collisions. Progressively, more types of energy were added to the definition of energy.
We have from the conservation of energy,
[tex]E_{i}[/tex] = [tex]E_{f}[/tex]
[tex]E_{i}[/tex] = [tex]\frac{-G(5*0.1)}{0.4}[/tex] - [tex]\frac{G(10*0.1)}{0.6}[/tex]
[tex]E_{i}[/tex] = [tex]\frac{-G(5*0.1)}{0.8}[/tex] - [tex]\frac{G(10*0.1)}{0.2}[/tex] + 1/2 × 0.1v²
∵ [tex]E_{i}[/tex] = [tex]E_{f}[/tex]
= 1/2 × 0.1 × v² = G (5×0.1) (1/0.8 - 1/0.4) + G (10 × 0.1) (1/0.2 - 1/0.6)
∴ v = 6.01 × 10⁻⁵ m/s
Speed of the object moved from its initial position is 6.01 × 10⁻⁵ m/s.
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