# Minimum Speeds for 100g Particles on Energy/Distance Graph

• Honore
In summary, using the principle of conservation of energy, the minimum speed (m/s) needed for a 100 g particle to go from point A to point B is 2 m/s. Similarly, the minimum speed (m/s) needed for the particle to go from point B to point A is also 2 m/s. Any position dependent force is considered a conservative force, meaning that the potential energy is already given as a function of the position. This allows us to ignore any resistance factors, such as friction, and focus solely on the starting and ending points to determine the minimum kinetic energy needed.
Honore
With reference to the attached "energy versus distance graph" of two particles;

a. What minimum speed (m/s) does a 100 g particle need at point A to reach point B?

b. What minimum speed (m/s) does a 100 g particle need at point B to reach point A?

Thank you.

#### Attachments

• energy versus distance graph.JPG
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Use conservation of energy. First find the minimum kinetic energy needed to go from A to B, then get the speed from that.

Galileo said:
Use conservation of energy. First find the minimum kinetic energy needed to go from A to B, then get the speed from that.

In order to find the minimum kinetic energy, I think I have to find the total work done referring to a "Force vs Distance" graph. But, how can "Force" be found from a graph which is not linear?

Work = $\int F dx$

Is this gravitational potential? In that case, its conservative, and you can ignore anything but the starting and ending points. You lost 2 Joules of PE to get from A to B, so you gained 2 Joules of KE.

$$KE = 1/2 mv^2$$

$$2 = 1/2 (100g) v^2$$

In one dimension, any position dependent force is conservative (the potential (or total?) energy is already given as a function of the position).

Isnt "position dependant force" part of the definition of "conservative force"? Say there was a resistance factor such as friction, the energy wouldn't be conserved then.

## What is the significance of minimum speeds for 100g particles on an energy/distance graph?

The minimum speed for 100g particles on an energy/distance graph represents the threshold at which these particles are able to overcome the energy barrier and move to a higher energy state. This is important in understanding the behavior and properties of these particles in various physical and chemical processes.

## How is the minimum speed for 100g particles determined on an energy/distance graph?

The minimum speed for 100g particles can be determined by finding the point on the energy/distance graph where the slope is zero. This indicates that the particles have just enough energy to overcome the energy barrier and transition to a higher energy state.

## What factors can affect the minimum speed for 100g particles on an energy/distance graph?

The minimum speed for 100g particles can be affected by several factors such as temperature, pressure, and the nature of the particles themselves (e.g. size, shape, composition). These factors can alter the energy barrier and thus impact the minimum speed required for the particles to transition to a higher energy state.

## How does the minimum speed for 100g particles on an energy/distance graph relate to the concept of activation energy?

The minimum speed for 100g particles on an energy/distance graph is directly related to the concept of activation energy. It represents the minimum amount of energy required for a reaction to occur or for the particles to transition to a higher energy state. The greater the activation energy, the higher the minimum speed required for the particles.

## What are some real-world applications of understanding the minimum speed for 100g particles on an energy/distance graph?

Understanding the minimum speed for 100g particles on an energy/distance graph has various real-world applications. For example, it can help in designing more efficient chemical reactions by determining the necessary energy input required. It is also vital in studying the behavior of particles in physical processes such as diffusion and osmosis. Additionally, it can aid in the development of new materials with specific properties based on the minimum speed required for particle transitions.

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