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Betty weighs 432 N and she is sitting on a playground swing seat that hangs 0.41 m above the ground. Tom pulls the swing back and releases it when the seat is 0.94 m above the ground. The acceleration of gravity is 9.8 m/s 2 . How fast is Betty moving when the swing passes through its lowest position? Answer in units of m/s.

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davidlcastiblanco

Answer:

v=3.22 m/s

Explanation:

This work is stored as gravitational potential energy. When Betty moves through the lowest position, that gravitational potential energy is converted to kinetic energy

[tex]m*g*h=\frac{1}{2}*m*v^2[/tex]

Resolve to v' so:

[tex]m*v^2=2*m*g*h[/tex]

[tex]v^2=2*g*h[/tex]

Now height is difference of both alture so

[tex]h=0.94m-0.41m[/tex]

[tex]h=0.53m[/tex]

replacing

[tex]v^2=\sqrt{2*9.8\frac{m}{s^2}*0.53m}=\sqrt{10.388\frac{m^2}{s^2}}[/tex]

[tex]v=3.22 \frac{m}{s}[/tex]

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