A 4\text{ kg} object is launched vertically upward from the ground. At a height of 20\text… — Armed Services Vocational Aptitude Battery (ASVAB)

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

$850\text{ J}$ Answer
B
$800\text{ J}$
C
$130\text{ J}$
D
$50\text{ J}$

Answer

The total mechanical energy at the exact moment it was launched is

850\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\text{-meter}

mark. Calculating the potential energy (

mgh = 800\text{ J}

) and the kinetic energy (

\frac{1}{2}mv^2 = 50\text{ J}

) yields a total mechanical energy of

850\text{ J}

Step-by-Step Solution

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\text{ m}

height.

Calculate the gravitational potential energy (

PE

) at the

20\text{-meter}

height.

PE = m \times g \times h = 4 \times 10 \times 20 = 800\text{ J}

To determine the energy stored due to the object's height.

Calculate the kinetic energy (

KE

) at the

20\text{-meter}

height.

KE = \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.

Sum the

PE

and

KE

to find the total mechanical energy.

800\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.

Key Concept

Conservation of Mechanical Energy

Question

Answer

Step-by-Step Solution

Key Concept

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