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# Work, Kinetic Energy and Potential Energy

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6.1. THE IMPORTANT STUFF
129
If we describe the motion of the end of the spring with the coordinate x and put the
origin of the x axis at the place where the spring exerts no force (the equilibrium position)
then the spring force is given by
F
x
= -kx
(6.11)
Here k is force constant, a number which is different for each ideal spring and is a measure
of its "stiffness". It has units of N/ m = kg/ s
2
. This equation is usually referred to as
Hooke's law. It gives a decent description of the behavior of real springs, just as long as
they can oscillate about their equilibrium positions and they are not stretched by too much!
When we calculate the work done by a spring on the object attached to its end as the
object moves from x
i
to x
f
we get:
W
spring
=
1
2
kx
2
i
-
1
2
kx
2
f
(6.12)
6.1.4
The Work­Kinetic Energy Theorem
One can show that as a particle moves from point r
i
to r
f
, the change in kinetic energy of
the object is equal to the net work done on it:
K = K
f
- K
i
= W
net
(6.13)
6.1.5
Power
In certain applications we are interested in the rate at which work is done by a force. If an
amount of work W is done in a time t, then we say that the average power P due to the
force is
P =
W
t
(6.14)
In the limit in which both W and t are very small then we have the instantaneous power
P , written as:
P =
dW
dt
(6.15)
The unit of power is the watt, defined by:
1 watt = 1 W = 1
J
s
= 1
kg·m
2
s
3
(6.16)
The watt is related to a quaint old unit of power called the horsepower:
1 horsepower = 1 hp = 550
ft·lb
s
= 746 W
One can show that if a force F acts on a particle moving with velocity v then the
instantaneous rate at which work is being done on the particle is
P = F · v = F v cos
(6.17)
where is the angle between the directions of F and v.

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Summary :

## If an amount of work W is done in a time t, then we say that the average power P due to the force is P = W t (6.14) In the limit in which both W and t are very small then we have the instantaneous power P , written as: P = dW dt (6.15) The unit of power is the watt, defined by: 1 watt = 1 W = 1 J s = 1 kg·m 2 s 3 (6.16) The watt is related to a quaint old unit of power called the horsepower: 1 horsepower = 1 hp = 550 ft·lb s = 746 W One can show that if a force F acts on a particle moving with velocity v then the instantaneous rate at which work is being done on the particle is P = F · v = F v cos (6.17) where is the angle between the directions of F and v.

Tags : spring,force,power,work,done,which,then,object,watt,particle,moes,end,614
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