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At the top of a giant swing on the gymnastics high bar, candy's velocity is 1 m/s, and she is 3.5 m high. if candy's mass is 50 kg, what is her total mechanical energy at this instant?

Respuesta :

skyluke89
The total mechanical energy is the sum of the kinetic energy and the gravitational potential energy:
[tex]E=K+U= \frac{1}{2}mv^2 +mgh[/tex]
where m=3.5 kg is Candy's mass, v=1 m/s is her velocity and h=3.5 m is her height. If we replace these numbers, we find the mechanical energy of the system:
[tex]E= \frac{1}{2} (50 kg)(1m/s)^2 + (50 kg)(9.81 m/s^2)(3.5 m)=1742 J =1.74 kJ [/tex]
nuhulawal20

At the top of the giant swing on the gymnastics high bar, candy's total mechanical energy is 1740J.

Given the data in the question;

  • Candy's velocity; [tex]v = 1 m/s[/tex]
  • Candy's height from the ground; [tex]h = 3.5m[/tex]
  • Candy's mass; [tex]m = 50kg[/tex]

Candy's total mechanical energy; [tex]M.E_c = \ ?[/tex]

Total Mechanical Energy (M.E) is the sum of both the potential energy and the kinetic energy of an object.

[tex]Mechanical \ Energy = Potential \ Energy + Kinetic \ Energy[/tex]

[tex]M.E = mgh + \frac{1}{2}mv^2[/tex]

Where m is the mass, g is gravitational acceleration( [tex]9.8m/s^2[/tex] ), h is the height and v is the velocity.

We substitute our values into the equation

[tex]M.E_c = ( 50kg * 9.8m/s^2*3.5m) + ( \frac{1}{2}* 50\ *(1m/s)^2)\\\\M.E_c = 1715kg.m^2/s^2 + 25kg.m^2/s^2\\\\M.E_c = 1740 kg.m^2/m^2\\\\M.E_c = 1740J\\[/tex]

Therefore, at the top of the giant swing on the gymnastics high bar, candy's total mechanical energy is 1740J

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