Power associated with net force

In summary, the conversation discusses how to prove that the power associated with the net force is equal to the rate of change of kinetic energy. The participants suggest using the definition of power and work, as well as the equation F_net=ma. After some clarification on the notation, it is concluded that the equation can be rewritten as P_F=(dK/dt), and that the solution is just a few steps away.
  • #1
REVIANNA
71
1

Homework Statement



How to prove :
[/B]
##P*F_net=((dK)/(dt))##
i.e. power associated with the net force is the rate of change of kinetic energy.

The Attempt at a Solution


[/B]
if I use the definition of power ans then that of work I get (m*a*ΔS )*(F_net)
further using F_net=ma
LHS= ##m^2*a^2*ΔS##

There is no question along with it for which I could have though about the system and forces.
so I am assuming const force and acceleration.
 
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  • #2
REVIANNA said:
P∗Fnet=((dK)/(dt))P*F_net=((dK)/(dt))
Is that product of force and power on LHS? If yes, the equation looks dimensionally incorrect.
Actually, if you solved dK/dt first, you'll get power.
 
Last edited:
  • #3
cnh1995 said:
Is that product of force and power on LHS? If yes, the equation looks dimensionally incorrect.
Actually, if you solved dK/dt first, you'll get power.

so sorry ,actually the F_net was written as the subscript P ,not their product
this makes complete sense now
##P_F=(dK/dt)##
 
  • #4
REVIANNA said:
so sorry ,actually the F_net was written as the subscript P which not their product
this makes complete sense now
##P_F=(dK/dt)##
Then I believe answer is a couple of steps away. Good luck..
 
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Likes REVIANNA

1. How is power related to net force?

Power is directly proportional to net force. This means that as the net force increases, the power also increases. This relationship can be mathematically represented by the formula P = F x v, where P is power, F is net force, and v is velocity.

2. How does power affect the motion of an object?

Power is the rate at which work is done, so it determines how quickly an object can change its motion. A greater power means the object can accelerate faster or perform work in a shorter amount of time. This is why powerful machines can move or lift heavy objects more quickly than weaker ones.

3. What units are used to measure power?

The standard unit of power is the watt (W), which is defined as one joule per second. Other common units include horsepower (hp), which is often used to measure the power of engines, and kilowatt (kW), which is used to measure larger amounts of power such as in electricity generation.

4. Can net force and power ever be equal?

No, net force and power are not the same thing and cannot be equal. Net force is a vector quantity that describes the overall force acting on an object, while power is a scalar quantity that describes the rate at which work is done. They have different units of measurement and represent different aspects of an object's motion.

5. How does friction affect the power associated with net force?

Friction is a force that opposes motion, so it can decrease the power associated with net force. This is because some of the energy produced by the net force is lost due to friction. In order to maintain a constant power output, the net force must increase to compensate for the loss of energy to friction.

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