# Conservation of mechanical energy (low difficulty)

• Oscar Wilde
In summary: For part C, you can use the same equation but plug in -13m for \Delta y and the velocity you found for part B as the initial velocity. This should give you a velocity of 22.4 m/s for part C.
Oscar Wilde

## Homework Statement

There is a rollercoaster. A car starts 35m "high" and descends to the ground. A.) What is the velocity at this point? The car continues an goes 28m above the ground. B.) calculate its velocity at this point. C.) If the car descends another 13m from this point, what is the velocity

Ignore Friction

mgy=1/2mv^2

## The Attempt at a Solution

using mgy= 1/2mv^2 i got the answer to a.), which is 26 m/s. But after this I became flustered and I do not know what to do to get its velocity if it goes 28m higher. I understand c. but I need the velocity at point B to get it!

I'm sorry I just figured it out for B.

I set 1/2mv^2=1/2mv^2+mgy and found my second velocity, which comes out to 11.7 roughly when using g=9.8

I would appreciate if someone would confirm my findings

I then set up the (square root of(1/2mv^2 + mgy-mgy)/.5)=v and came out with 20 m/s for C.

Oscar Wilde said:

## Homework Statement

There is a rollercoaster. A car starts 35m "high" and descends to the ground. A.) What is the velocity at this point? The car continues an goes 28m above the ground. B.) calculate its velocity at this point. C.) If the car descends another 13m from this point, what is the velocity

Ignore Friction

mgy=1/2mv^2

## The Attempt at a Solution

using mgy= 1/2mv^2 i got the answer to a.), which is 26 m/s. But after this I became flustered and I do not know what to do to get its velocity if it goes 28m higher. I understand c. but I need the velocity at point B to get it!

You're on the right track, think about conservation of energy
$$\Delta U = m g \Delta y$$
$$\Delta K = \frac{1}{2} m(v_f ^2-v_i^2)$$
Thus $$\Delta K + \Delta U = 0$$
Thus $$-m g \Delta y +\frac{1}{2} m v_i^2= \frac{1}{2} m v_f^2$$

I also got 11.7 for part B.

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

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

## 2. How is mechanical energy conserved?

Mechanical energy is conserved through the interplay of potential energy and kinetic energy. Potential energy is the energy an object has due to its position or configuration, while kinetic energy is the energy an object has due to its motion. As an object moves, its potential energy may decrease while its kinetic energy increases, but the total amount of mechanical energy remains constant.

## 3. What are some examples of mechanical energy conservation in everyday life?

There are many examples of mechanical energy conservation in everyday life, such as swinging on a playground swing, riding a bicycle, or throwing a ball. In each of these scenarios, the potential energy of the object (the swing, the cyclist, the ball) is converted into kinetic energy as it moves.

## 4. Is mechanical energy conservation always true?

In ideal situations, where there is no external force acting on a system, mechanical energy conservation is always true. However, in the real world, there is always some form of energy loss due to friction or other external forces. This means that in most cases, mechanical energy is not completely conserved, but the concept still holds true as the total energy in a closed system remains constant.

## 5. How is the conservation of mechanical energy related to the law of conservation of energy?

The conservation of mechanical energy is a specific application of the law of conservation of energy, which states that the total energy in a closed system remains constant. Mechanical energy conservation specifically focuses on the exchange and transformation of potential and kinetic energy within a system, while the law of conservation of energy applies to all forms of energy in a closed system.

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