**More energy and Hooke's law**

From last time we went through 2 derivations on how Mechanical

Energy is conserved. Specifically kinetic and gravitational potential

energy. The one was a quick little calculation from kinematics

the other a bit more elegant with freefall.

This could have lead one to believe that only freefall conserves

mechanical energy.

Not true. Your book decides to derive conservation of mechanical

energy one more time. And you get the same result:

This again says that the initial Kinetic, and gravitational potential

Energies are conserved.

The reason for the repeat is that this derivations shows that

mechanical energy is conserved along any frictionless surface

regardless of shape.

Note: For energy calculations

the y-axis is vertical. Gravity

depends on height above surface

of the earth.

**Ballistic Pendulum**

**As a side note.**

Our conservation of mechanical energy equations

says this

not this

There is a negative sign missing here, you'll note

that one change will have a positive amount while

the other change is negative.

Our conservation of mechanical energy equations

says this

not this

There is a negative sign missing here, you'll note

that one change will have a positive amount while

the other change is negative.

**What about a box sliding across the desk?**

**Hooke's Law**

Springs are an example of a restoring force.

If you pull the spring, it pulls back,

If you compress the spring it pushes back.

Each spring system has a position of equilibrium

for example, a hanging mass on a spring is in equilibrium

when gravity is pulling down and the spring force is

pulling up.

This displacement is proportional to the force

of the spring.

**This equation is Hooke's Law.**

**Note we can solve for k by hanging different**

masses and measuring the displacement.

masses and measuring the displacement.

A pendulum is made by tying a 500 g ball to a 75 cm string. The pendulum is pulled 30 degrees to ones side then released.

What is the ball's speed at the lowest point of its trajectory?

To what angle does the pendulum swing on the other side?

**A. d>a>c>b B. c=d>a=b C. d>c>a>b D. d=c=b=a**

A. a=b=c B. a>b>c C. c>b>a

"is there a universal energy equation that can be used?"

"What happens to springs that are stretched or compressed to far? and why does Hooke's law no longer apply to them?"

"Hooks law can apply to anything elastic right? Like a bow? Or diving board?"

"It seems like a lot of this section is based on the fact that energy is conserved. Is it realistic to assume that energy is conserved in most systems? What are some examples of energy not being conserved?"

"why is Hookes law so important for everyday life?"

"How is Hooke's law a restoring force?"

1.4 m/s

30

A 5.0 kg mass hanging from a spring scale is slowly lowered onto a vertical spring, as shown. The scale reads in newtons.

A. What does the spring scale read just before the mass touches the lower spring?

B. The scale reads 20 N when the lower spring has been compressed 2.0 cm. What is the value of the spring constant for the lower spring?

C. At what compression length will the scale read zero?

49 N

1450 N/m

3.38 cm

A 1500 kg car traveling at 10 m/s suddenly runs out of gas while approaching the valley shown here. The alert driver immediately puts the car in neutral so that it will roll. What will be the car's speed as it coasts into the gas station on the other side of the valley?

1.41 m/s