# Work With Regards to Velocity

• ddelaiarro
In summary, the conversation revolved around the debate of whether running or walking for the same distance burns more calories. The argument was based on the equation W = F * d, where W represents work, F represents force, and d represents distance. The speaker argued that since the same mass is moved across the same distance, the same force is exerted, making the work output the same regardless of velocity. The colleague was convinced of this approach, but the speaker also mentioned the additional energy spent in running vs walking, such as heat output and changes in temperature.

#### ddelaiarro

You'll have to excuse me if this issue has been discussed here before. I did about 30 minutes worth of searching and didn't come upon it, so I decided to post.

A colleague and I had a lengthy discussion today on whether running a set distance spends more calories (energy) than walking that same distance.

My main argument centered around moving a mass over a distance.

My contention is that work is the product of force and distance:

W = F * d

If the same mass, m, is moved across the same distance, d, then the same force, F, is exerted. The hinge point of my argument is the assumption that your acceleration/deceleration is instantaneous.

If you look at the free body diagram, you'll note that you have force acting in two axis on the mass.

In the x-axis, you have the applied force, F, and the friction force, F_f. According to Newton's Second Law, a body in motion will stay in motion unless acted upon. Hence, in order to keep a constant velocity,

F = F_f hence $$\Sigma$$ F_x=0

In the y-axis, there's a gravitational force,

F_g = m * g

and the equal and opposite normal force, F_N

F_g = F_N hence $$\Sigma$$ F_y=0

The kinematic coefficient of fricition, u, is the same, regardless of velocity. The equation for friction force is:

F_f = F_N * u * cos(theta) <-- Theta being the angle at which the plane the mass is on is at. Assume a flat plain (cos0 = 1) for simplicity here.

Regardless of velocity, u and F_N are the same, hence F_f is the same.

So, if F_f is the same, F is the same. And, in the end,

W = F * d produces the same product regardless of velocity.

In the end, I convinced my coworker that my approach was correct. Although, he didn't buy the end result.

I'd love to hear some of your thoughts on this subject.

Consider the heat output from someone who just ran x vs someone who just caught up to that person by walking. The work done in transporting the body is the same (assuming exactly equal body masses) however there is other energy that is spent. You have to consider total energy difference, dE = dK + d(k*Temperature) in this case.

Dear colleague,

Thank you for bringing up this interesting topic. I agree with your argument that work is the product of force and distance, and that the same work is done regardless of the velocity at which the distance is covered. This is because the force and distance remain constant, and according to the laws of physics, work is only done when there is a displacement in the direction of the applied force.

However, I also understand your colleague's skepticism about the end result. It is important to consider that while the work done may be the same, the energy expenditure may not necessarily be equal. This is because the human body has different energy requirements for different activities, and the intensity and duration of the activity can also affect the amount of energy expended.

For example, running may require more energy expenditure than walking due to the increased effort and intensity involved. Additionally, the body may also adapt and become more efficient at certain activities, leading to a decrease in energy expenditure over time.

In conclusion, while your argument about work and velocity is valid, it is important to also consider other factors that may affect energy expenditure. I hope this helps in your further discussions on this topic.

Best regards,

## 1. What is velocity and how is it related to work in science?

Velocity is a measure of an object's speed and direction. In science, velocity is related to work through the concept of power. Work is the amount of energy transferred when a force is applied to an object and causes it to move a certain distance. The greater the velocity of an object, the more work it can do.

## 2. How do you calculate the velocity of an object?

The velocity of an object can be calculated by dividing the distance traveled by the time it took to travel that distance. This is represented by the equation v = d/t, where v is velocity, d is distance, and t is time. Velocity is typically measured in units of distance per time, such as meters per second or miles per hour.

## 3. How does velocity affect the amount of work that can be done?

Velocity is directly proportional to the amount of work that can be done. This means that as velocity increases, the amount of work that can be done also increases. This is because an object with a higher velocity has more energy and therefore can transfer more energy when work is done on it.

## 4. Can velocity be negative in the context of work?

Yes, velocity can be negative in the context of work. Negative velocity simply means that an object is moving in the opposite direction of a chosen reference point. This does not affect the amount of work that can be done, as negative velocity still represents the speed and direction of an object.

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

In the context of work, velocity is related to the conservation of energy through the law of conservation of energy. This law states that energy cannot be created or destroyed, only transferred from one form to another. In the case of work, the energy used to do work on an object is transferred to that object in the form of kinetic energy, which is represented by velocity. This means that the total amount of energy in a system (including both the object doing the work and the object being worked on) remains constant.