An object of mass 40 kg is raised to a height of 5 m above the ground. What is its potential energy initially and at halfway point? If the object is allowed to fall, find its kinetic energy when it is halfway down. Potential energy at the beginning is 1960 J and at halfway point is 960 J. Correct answer: B 1960 J, 960 J, 1000 J
Question
An object of mass 40 kg is raised to a height of 5 m above the ground. What is its potential energy initially and at halfway point? If the object is allowed to fall, find its kinetic energy when it is halfway down.
Potential energy at the beginning is 1960 J and at halfway point is 960 J.
Correct answer: B $1960 \mathrm{~J}, 960 \mathrm{~J}, 1000 \mathrm{~J}$
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Answer
The correct option is: C $1960 , \mathrm{J}, 980 , \mathrm{J}, 980 , \mathrm{J}$
Let's break down the calculations to find the potential and kinetic energy:
Gravitational Potential Energy
Gravitational potential energy is given by the formula: $$ \mathrm{PE} = \mathrm{mgh} $$
Where:
- $\mathrm{m}$ is the mass of the object $= 40 , \mathrm{kg}$
- $\mathrm{g}$ is the acceleration due to gravity $= 9.8 , \mathrm{m/s}^2$
- $\mathrm{h}$ is the height above the ground $= 5 , \mathrm{m}$
Calculating the potential energy at the initial height: $$ \mathrm{PE}_\text{initial} = 40 \times 9.8 \times 5 = 1960 , \mathrm{J} $$
At the Halfway Point
When the object is halfway down, the height is: $$ \frac{5 , \mathrm{m}}{2} = 2.5 , \mathrm{m} $$
The potential energy at this halfway point then is: $$ \mathrm{PE}_\text{halfway} = 40 \times 9.8 \times 2.5 = 980 , \mathrm{J} $$
Kinetic Energy at the Halfway Point
According to the law of conservation of energy, the total mechanical energy remains constant if only conservative forces are acting (here, only gravity). Thus, the sum of potential energy and kinetic energy at any point is equal to the total energy at the beginning.
Given that the initial potential energy is $1960 , \mathrm{J}$, when the object has fallen halfway, its potential energy is $980 , \mathrm{J}$.
The rest of the energy must be in the form of kinetic energy: $$ \mathrm{KE}\text{halfway} = \mathrm{Total \ Energy} - \mathrm{PE}\text{halfway} $$
Therefore: $$ \mathrm{KE}_\text{halfway} = 1960 , \mathrm{J} - 980 , \mathrm{J} = 980 , \mathrm{J} $$
So, at the halfway point, the potential energy is $980 , \mathrm{J}$ and the kinetic energy is also $980 , \mathrm{J}$.
Conclusion
- Potential energy at the beginning: $1960 , \mathrm{J}$
- Potential energy at the halfway point: $980 , \mathrm{J}$
- Kinetic energy at the halfway point: $980 , \mathrm{J}$
Therefore, the correct answer is C $1960 , \mathrm{J}, 980 , \mathrm{J}, 980 , \mathrm{J}$.
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