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Zorluk: Çok zorWork, Energy, and Power

A 4 kg4\text{ kg} object is launched vertically upward from the ground. At a height of 20 meters20\text{ meters}, it is traveling at a speed of 5 m/s5\text{ m/s}. Assuming acceleration due to gravity is 10 m/s210\text{ m/s}^2 and ignoring air resistance, what was the total mechanical energy of the object at the exact moment it was launched?

  1. 850 J850\text{ J}Cevap
  2. B
    800 J800\text{ J}
  3. C
    130 J130\text{ J}
  4. D
    50 J50\text{ J}

Cevap

The total mechanical energy at the exact moment it was launched is 850 J850\text{ J}.
According to the law of conservation of energy, the total mechanical energy remains constant throughout the object's flight in the absence of air resistance. Therefore, the total energy at launch equals the sum of its kinetic and potential energy at the 20-meter20\text{-meter} mark. Calculating the potential energy (mgh=800 Jmgh = 800\text{ J}) and the kinetic energy (12mv2=50 J\frac{1}{2}mv^2 = 50\text{ J}) yields a total mechanical energy of 850 J850\text{ J}.

Adım Adım Çözüm

1
Identify the relevant physical principle.
Total Mechanical Energy = Potential Energy + Kinetic Energy. This total is conserved.
By the law of conservation of energy, the total energy at launch is exactly equal to the total energy at the 20 m20\text{ m} height.
2
Calculate the gravitational potential energy (PEPE) at the 20-meter20\text{-meter} height.
PE=m×g×h=4×10×20=800 JPE = m \times g \times h = 4 \times 10 \times 20 = 800\text{ J}
To determine the energy stored due to the object's height.
3
Calculate the kinetic energy (KEKE) at the 20-meter20\text{-meter} height.
KE=12mv2=12×4×52=50 JKE = \frac{1}{2}mv^2 = \frac{1}{2} \times 4 \times 5^2 = 50\text{ J}
To determine the energy the object possesses due to its current upward motion.
4
Sum the PEPE and KEKE to find the total mechanical energy.
800 J+50 J=850 J800\text{ J} + 50\text{ J} = 850\text{ J}
The total mechanical energy at this height equals the mechanical energy at the exact moment of launch.

Anahtar Kavram

Conservation of Mechanical Energy
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Konular

Work, Energy, and Power

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