# Question about the Conservation of Energy

• nicholz
In summary, according to the law of conservation of energy, the velocity of a cart that rolls down a 5m ramp and then flies off a 3m high table would be the square root of 2gh, where h is the difference in height (8m).
nicholz
If a cart rolled down a ramp 5 meters high and flew off a a table at 3 meters high, what would its velocity be?

please let me know where i go wrong, i was using the law of conservation of energy

mgh1=mgh2+1/2mv2
mg(h1-h2)=1/2mv2
v=square root of 2g(h1-h2)

where h1=5 and h2=3

i plugged in numbers for the variables and i can't seem to get it to work out. is the equation i came up with correct?
edit: i was thinking that it should come out to the square root of 2gh. would that be right though? can i consider the release height to be the "0" height here?

Last edited:
Yes your equation is correct, though since the ramp is 5m high and then the table is 3m high, shouldn't h1=8m?

Your equation is correct, but you have made a mistake in plugging in the values for h1 and h2. The height difference (h1-h2) should be 2 meters, not 8 meters. This means that the final equation should be v=square root of 2gh, where g is the acceleration due to gravity (9.8 m/s^2). This would give you a final velocity of approximately 6.26 m/s.

Also, it is important to note that this equation assumes that there is no loss of energy due to friction or air resistance. In real life, some energy would be lost and the velocity of the cart would be slightly lower than the calculated value.

## 1. What is the definition of conservation of energy?

The conservation of energy is a fundamental law of physics that states that energy cannot be created or destroyed, only transferred or transformed from one form to another.

## 2. Why is the conservation of energy important?

The conservation of energy is important because it helps us understand how energy behaves in various systems and allows us to make predictions and calculations about the behavior of physical processes. It also plays a crucial role in the development of new technologies and sustainable energy sources.

## 3. How does the conservation of energy relate to the first law of thermodynamics?

The first law of thermodynamics states that the total energy in a closed system remains constant. This is essentially another way of stating the conservation of energy principle. It means that energy can be converted from one form to another, but the total amount of energy in the system remains the same.

## 4. What are some real-life examples of the conservation of energy?

Some real-life examples of the conservation of energy include a swinging pendulum, a bouncing ball, and a rollercoaster. In all of these scenarios, the total amount of energy remains constant, even though it may change forms (such as potential energy to kinetic energy).

## 5. Are there any exceptions to the conservation of energy?

The conservation of energy is a fundamental law of physics and has been rigorously tested and observed in countless experiments. Therefore, there are no known exceptions to this principle. However, in certain situations, it may appear that energy is being created or destroyed, but in reality, it is simply being transferred or transformed in ways that may not be immediately apparent.

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