Download Spring Time The force applied by a spring is also conservative

The force applied by a spring is also conservative
Spring Time
1
Total Energy of a spring in motion
Substitute for velocity and position
2
The force applied by a spring is also conservative
The potential energy curve for a spring:
A spring and block are oriented vertically
Block=1.7kg, Spring Constant k=955N/m
Initially, the spring is compressed d=4.60 cm and
the block is at rest.
When the block is released, it accelerates
upward.
Find the speed of the block when the spring has
returned to its equilibrium position.
initial mechanical energy
Ei  U i  K i  mgd  12 kd 2  0
Solve for v
final mechanical energy
Ef  U f  K f  0  0  12 mv
mgd  12 kd 2  12 mv 2
2
v  kd 2 /m  2 gd
Given numerical values
v  0535 m/s
Conservative and Nonconservative Forces
Conservative force: the work it does is stored in
the form of energy that can be released at a later
time
Example of a conservative force: gravity, springs
Example of a nonconservative force: friction, air
resistance
Also: the work done by a conservative force
moving an object around a closed path is zero;
this is not true for a nonconservative force
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Work Done by Nonconservative Forces
In the presence of nonconservative forces, the
total mechanical energy is not conserved:
Solving,
Work Done by Nonconservative Forces
Consider the block sliding down an incline.
Initially the block is on flat section with no
friction. It has both kinetic energy and
potential energy wrt the bottom of the
ramp.
The block slides down because gravity
does positive work on it, converting the
potential energy to kinetic energy.
At the same time, friction does negative
work on the block, dissipating some of
its kinetic energy to non-mechanical
energy
The system’s final energy is party
kinetic and partly non-mechanical
(thermal).
Energy has been conserved, but not mechanical energy.
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m
vi = 0
vi = 0
m = 50g
h = 30cm
vi = 0
vf = 1.5m/s
h
What is the amount of
energy lost to the
nonconservative force?
y
vf = 1.5m/s
x
8
Find the Diver’s Depth
A 95.0 kg diver steps off a diving
board and drops into the water, 3.00 m
below. At some depth d below the
water’s surface, the diver comes to
rest.
If the nonconservative work done
on the diver is Wnc = 5,120 J, what is
the depth d?
Ei  mgh  0  mgh
E f  mg (d )  0  mgd
Wnc  E  E f  Ei  mgd  mgh
d  (Wnc  mgh) / mg  2.49 m