Unlock the Mystery of Work & Energy: Zero Acceleration, Constant Velocity

In summary: So the object is not being accelerated, but it is being moved at a constant velocity, and work is being done on it. So the work-energy theorem does NOT apply here, because the object is not being accelerated, and hence, KE is not changing. No matter how much time passes, the KE of the object will remain 0, and no change in KE means no change in PE, since the object is not moving up or down. So KEi+PEi=KEf+PEf. In summary, the concept of work and its relationship to force, displacement, and acceleration is a fundamental concept in understanding the principles of work and energy. Negative work can be done by a force, and the work-energy theorem does not
  • #1
quicksilver123
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https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/v/work-and-energy--part-2

I was watching a video at Khan Academy on Work & Energy (link above).

At 2:50, he describes a situation with an elevator doing work against gravity.

My question is pretty simple:

If the acceleration (and hence, net force) is equal to zero (the upwards force cancelling out the downwards force due to gravity), how did the upwards force produce any movement at all?

The constant velocity means there's no acceleration, and that's fine.

But shouldn't there be no movement at all?

eg. [let down be negative]
If I hold my hand out and apply an upwards force of F=mg, wouldn't that merely counteract downwards acceleration due to gravity (F=-mg)? Wouldn't my hand merely stay still in the vertical plane?
Or, in a similar example more related to the one in the video, if my hand was held out and accelerating upwards due to a force, and that force changed to be equal and opposite to the force of gravity, would my hand continue to move upwards (with zero acceleration) at a constant velocity?

This is a conceptual problem that's been bugging me... even though the math supports what coursework teachers. I need help grasping this concept.
 
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  • #2
quicksilver123 said:
https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/v/work-and-energy--part-2

I was watching a video at Khan Academy on Work & Energy (link above).

At 2:50, he describes a situation with an elevator doing work against gravity.

My question is pretty simple:

If the acceleration (and hence, net force) is equal to zero (the upwards force cancelling out the downwards force due to gravity), how did the upwards force produce any movement at all?

The constant velocity means there's no acceleration, and that's fine.

But shouldn't there be no movement at all?

eg. [let down be negative]
If I hold my hand out and apply an upwards force of F=mg, wouldn't that merely counteract downwards acceleration due to gravity (F=-mg)? Wouldn't my hand merely stay still in the vertical plane?
Or, in a similar example more related to the one in the video, if my hand was held out and accelerating upwards due to a force, and that force changed to be equal and opposite to the force of gravity, would my hand continue to move upwards (with zero acceleration) at a constant velocity?

This is a conceptual problem that's been bugging me... even though the math supports what coursework teachers. I need help grasping this concept.
Once movement upwards is established, it takes a net force of zero to maintain the upward motion at a constant velocity. Newton's first law should tell you this. His second law also confirms this.
 
  • #3
Ah. Simple enough - inertia.

It would take a downwards force greater than gravity to cause my hand to decelerate to a velocity of zero (at which point it would begin to fall).

Thanks. I know the laws work in math (and therefore in nature). I guess its just a matter of thinking of a variety examples until those laws are ingrained in my mind.
 
  • #4
I know these are stupid questions - I'm just having trouble wrapping my head around some of these core concepts... and I need to master them before moving on.

A similar question - maybe someone can give me an example or something.

Work = displacement times force
w=df

(let the direction of motion be positive)

Let's say an object is sliding across my desk. How it started sliding doesn't matter.
It experiences negative acceleration due to kinetic friction.

Since f=ma
w=dmaWould negative work have been done, since acceleration is negative? Or are these absolute values?

Another one -
If I were to move an object (m=0.1kg) across my desk 0.5m with my hand at a constant speed (a=0), would zero work be done? After all, since a=0, w=0 as well... no?
 
  • #5
quicksilver123 said:
I know these are stupid questions - I'm just having trouble wrapping my head around some of these core concepts... and I need to master them before moving on.

A similar question - maybe someone can give me an example or something.

Work = displacement times force
w=df

(let the direction of motion be positive)

Let's say an object is sliding across my desk. How it started sliding doesn't matter.
It experiences negative acceleration due to kinetic friction.

Since f=ma
w=dma


Would negative work have been done, since acceleration is negative? Or are these absolute values?
work, a scalar quantity, can be positive or negative, and is defined as the dot product of the force and displacement vectors, (f)(d)(costheta), where theta is the angle between the 2 vectors. In this case, the displacement is rightward and the force is leftward, so theta is 180 degrees, and hence, negative work is done by the friction force. Work done by a force does not necessarily require acceleration, however, as noted below in your next question.
Another one -
If I were to move an object (m=0.1kg) across my desk 0.5m with my hand at a constant speed (a=0), would zero work be done? After all, since a=0, w=0 as well... no?
The work done by the NET force is 0, Since the NET force is 0. So you can say that the total or net work done on the object by all forces acting on it is 0. But the pushing force of your hand on the object does positive work , and the force of the equal and opposite friction force acting on the object does negative work of the same magnitude, so together, the sum total of the work done on the object is 0.
 

FAQ: Unlock the Mystery of Work & Energy: Zero Acceleration, Constant Velocity

What is the definition of work and energy?

Work is a measure of the force required to move an object a certain distance, while energy is the ability to do work. In simpler terms, work is the result of applying a force to an object and causing it to move, and energy is what allows that work to be done.

What is the relationship between work and energy?

The relationship between work and energy is that work is a form of energy. When work is done on an object, energy is transferred to that object. The amount of work done is equal to the change in energy of the object.

How does zero acceleration affect work and energy?

If an object has zero acceleration, it means that its velocity is constant. In this case, the work done on the object is equal to the change in its kinetic energy. This is because there is no change in the object's velocity, so there is no change in its kinetic energy.

How can we calculate work and energy in a zero acceleration scenario?

To calculate work and energy in a zero acceleration scenario, we can use the formula W = Fd, where W is work, F is the force applied, and d is the distance the object moves. We can also use the formula E = 1/2mv2 to calculate the kinetic energy of the object, where m is the mass of the object and v is its velocity.

What are some real-life examples of zero acceleration, constant velocity situations?

Some real-life examples of zero acceleration, constant velocity situations include driving a car at a constant speed on a straight road, a ball rolling along a flat surface with no friction, and a satellite orbiting the Earth at a constant speed.

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