Answer:
U = 8.30×10-⁹J
Explanation:
m1 = m2 = 5.00kg masses of the spheres
d = 15.0cm = 15×10-²m
r = 5.10cm = 5.10×10-²m
R = d + r = 15×10-² + 5.10×10-²
R = 20.10 ×10-²m = 0.201m
G = 6.67×10-¹¹Nm²/kg²
U = Gm1×m2/R = potential energybetween the spheres
U = 6.67×10-¹¹×5.00×5.00/0.201
U = 8.30×10-⁹J
The gravitational potential energy between the steel balls is [tex]8.29 \times 10^{-9} \;\rm J[/tex] and their speed upon impact is [tex]4.07 \times 10^{-5} \;\rm m/s[/tex].
Given data:
The mass of each spherical steel ball is, m'=m'' = 5.00 kg.
The center to center distance of separation is, d = 15 cm = 0.15 m.
And the radius of each sphere is, r = 5.10 cm. = 0.051 m.
The energy possessed by any body due to its position at gravitational field is known as gravitational potential energy. Its expression is,
[tex]U = \dfrac{G \times m'\times m'' }{(r+d)}[/tex]
G is the universal gravitational constant.
Solving as,
[tex]U = \dfrac{6.67 \times 10^{-11} \times 5\times 5' }{(0.051+0.15)}\\\\U=8.29 \times 10^{-9} \;\rm J[/tex]
Now, apply the conservation of energy as,
gravitational potential energy = kinetic energy
[tex]U = KE\\8.29 \times 10^{-9}= \dfrac{1}{2} \times (m''+m') \times v^{2} \\\\8.29 \times 10^{-9}= \dfrac{1}{2} \times (5+5) \times v^{2} \\\\v = 4.07 \times 10^{-5} \;\rm m/s[/tex]
Thus, we can conclude that the gravitational potential energy between the steel balls is [tex]8.29 \times 10^{-9} \;\rm J[/tex] and their speed upon impact is [tex]4.07 \times 10^{-5} \;\rm m/s[/tex].
Learn more about the gravitational potential energy here:
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