Help to understand the concept of Power

This is why you get tired just holding an object.In summary, Power is described as the Velocity at which Force is applied to an object (P=F*d/t). However, the force and velocity are not independent as the force applied does affect the velocity of the object. In order to calculate power, one must use the net force on the object and the distance it is moved. In cases of equilibrium, where there is no net force on the object, no work is performed on the object, but work is still performed on the person holding the object due to the inefficiency of the human body.
  • #1
AllStar
1
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Power is described as the Velocity at which Force is applied to an object (P=F*d/t)

However, how are the Force and Velocity independent? Doesn't the Force applied affect the Velocity of the object?

For example, let's say you want to lift a 19.62N (2kg*9.81m/s^2) object upwards 1 meter in 1 second. The way I see the problem solved online is that you would need 19.62W = (19.62N*1m/s). However, with this applied Force the object is in equilibrium (and not moving or moving at an arbitrary constant velocity), so the work and power would be zero.

I must have something wrong here. Thanks.
 
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  • #2
The object gains potential energy as it rises. Gravity can be considered a fictitious force.
 
  • #3
AllStar said:
moving at an arbitrary constant velocity), so the work and power would be zero.
If it's moving at constant velocity, then the work and power aren't zero.
 
  • #4
AllStar said:
Power is described as the Velocity at which Force is applied to an object (P=F*d/t)

That's a very bad definition .

There are formal definitions of Power but for practical purposes :

Power is rate of doing work .
or
Power is rate of transfer of energy from a source to a sink .
 
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  • #5
AllStar said:
Power is described as the Velocity at which Force is applied to an object (P=F*d/t)

However, how are the Force and Velocity independent? Doesn't the Force applied affect the Velocity of the object?

Yes, the force would affect the velocity of the object, but it doesn't matter. That fact is already "built-in" to work and power. For example, applying a net force of 10 Newtons for 10 seconds on a 1kg object:

##a = \frac{f}{m} = \frac{10}{1} = 10 m/{s^2}##
##v = v_0 + at = 0 + 10*10 = 100 m/s##

The distance the object moves over this time period is given by:
##x = x_0 + v_0t + 1/2at^2 = 0 + 0 + 1/2*10*10^2 = 500 m##

The work required to get the object up to 100 m/s is just the same as its kinetic energy.
##k_e = 1/2mv^2 = 1/2*1*100^2 = 5,000 J##

We can also calculate the work done using the force and the distance:
##W = f*d = 10 * 500 = 5,000 J##

Power:
##P = W/t = 5,000/10 = 500 W##

AllStar said:
For example, let's say you want to lift a 19.62N (2kg*9.81m/s^2) object upwards 1 meter in 1 second. The way I see the problem solved online is that you would need 19.62W = (19.62N*1m/s). However, with this applied Force the object is in equilibrium (and not moving or moving at an arbitrary constant velocity), so the work and power would be zero.

You need to use the net force on the object in your calculation. In equilibrium there is no net force and no work is performed on the object by any of the forces. Note that you will still expend energy and perform work on yourself because your body is not a perfectly efficient machine. Your muscles fibers constantly contract and relax just to hold an object at rest, your bones and muscles stretch and bend, the chemical reactions powering your muscles release a lot of energy simply as heat, etc.
 

FAQ: Help to understand the concept of Power

What is power?

Power is the ability to influence or control the behavior of others, either through physical force or through social, economic, or political means.

What are the different types of power?

There are five main types of power: coercive power, reward power, legitimate power, expert power, and referent power. Coercive power is based on fear and the ability to punish. Reward power is based on the ability to provide incentives. Legitimate power is based on one's position or role. Expert power is based on knowledge, skills, or expertise. Referent power is based on admiration, respect, or likability.

How is power measured?

Power can be difficult to measure as it is subjective and often context-dependent. However, some common ways of measuring power include looking at an individual or group's access to resources, their ability to make decisions and influence others, and their level of control over their own lives and the lives of others.

Can power be shared?

Yes, power can be shared among individuals or groups. This is known as distributed power or shared power. In this model, power is not held by one person or group, but is instead dispersed among multiple actors who work together to make decisions and influence outcomes.

What is the relationship between power and authority?

Power and authority are often used interchangeably, but they are not the same thing. While power refers to the ability to influence or control, authority refers to the legitimate right to do so. Authority is often derived from one's position or role, while power can be gained through various means. However, power and authority can also intersect, with those in positions of authority often having more power to influence others.

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