Conservation of Energy in Gravity

In summary, the final speed of the boy at the bottom of the roller coaster can be calculated using the equation v = √2gh, where g is the acceleration due to gravity and h is the vertical distance the boy falls. If the initial speed (u) is 0, the final speed (v) will be 19.8 ms-1. If the initial speed is 5 ms-1, the final speed will be 20.4 ms-1. This is because the formula changes to v^2 = u^2 +2gh when the initial velocity is not 0.
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Homework Statement


A boy at the top of a roller coaster falls through a vertical distance of 20m. What is the final speed of the boy if:
a) His initial speed was 0
b) His initial speed was 5 ms-1


Homework Equations


GPE at top = KE at bottom
mgh = 1/2mv^2
gh = 1/2v^2
v = √2gh

if the initial velocity (u) was not equal to zero, the maths becomes slightly different

initial total energy = final total energy
1/2mu^2 + mgh = 1/2mv^2

therefore...

v^2 = u^2 + 2gh


The Attempt at a Solution



a) 2x9.8x20 = 392

b) 5^2 + 2x9.8x20 = 417


The answers are:
a) 19.8 ms-1
b) 20.4 ms-1
What on Earth am I doing wrong... what can I do... or what? D: I just don't understand!
 
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  • #2
If v2=392 m2/s2, what is v?
 
  • #3
I love you and your wisdom. :D
Thankyou so much, you've really made my day!
 

FAQ: Conservation of Energy in Gravity

What is the conservation of energy in gravity?

The conservation of energy in gravity is a fundamental law in physics which states that the total energy in a closed system remains constant over time. This means that energy cannot be created or destroyed, only transferred or converted from one form to another.

How does gravity affect energy conservation?

Gravity plays a crucial role in energy conservation as it is responsible for the potential energy of an object. As an object is raised, it gains potential energy due to the force of gravity. This potential energy is then converted into kinetic energy as the object falls, and the total energy of the system remains constant.

Can energy be lost in a gravitational system?

No, energy cannot be lost in a gravitational system. According to the law of conservation of energy, the total energy of a system must remain constant. Energy may seem to be lost in a gravitational system if it is converted into a different form, such as thermal energy due to friction, but the total amount of energy remains the same.

How is the conservation of energy in gravity applied in real life?

The conservation of energy in gravity is applied in various real-life situations, such as the motion of objects on Earth's surface, the orbits of planets around the sun, and the motion of satellites in space. It is also crucial in understanding the efficiency of machines and the production of renewable energy sources.

What would happen if the conservation of energy in gravity did not hold true?

If the conservation of energy in gravity did not hold true, it would have a significant impact on the universe. It would mean that energy could be created or destroyed, leading to unpredictable and chaotic behavior of objects in the universe. This would result in the breakdown of fundamental laws of physics, making it impossible for life to exist as we know it.

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