1. Potential Energy and Energy Conservation
Chapter 7
Potential Energy and Energy Conservation

2. Potential Energy
Work done by gravity:
W=mg (Y2-Y1)

3. Work done moving up Work done by hand/normal force against gravity:
W=mg (Y2-Y1)
(If no acceleration)
The work by you turns into work by gravity then KE

4. Potential energy: The energy available to “do damage”
Back to swing story:
A 100kg boy swings from a tire swing of
Length 3[m]. The angle at the beginning is 53 degrees.
a. What is the speed at the bottom?
b. What is the tension in the string?

5. Add Elastic Energy
As shown last week: When x is positive (spring is stretched), F is negative
When x is 0 (at the equilibrium position), F is 0
When x is negative (spring is compressed), F is positive

6. Hooke’s Law
The force exerted by the spring is always directed opposite to the displacement from equilibrium
F is called the restoring force
If the block is released it will oscillate back and forth between –x and x

7. Work Done by a Spring Identify the block as the system
Calculate the work as the block moves from xi = - xmax to xf = 0
The total work done as the block moves from
–xmax to xmax is zero

8. Spring with an Applied Force
Suppose an external agent, Fapp, stretches the spring
The applied force is equal and opposite to the spring force
Fapp = -Fs = -(-kx) = kx
Work done by Fapp is equal to ½ kx2max

9. Energy bar diagram, problem 2
A block of mass m=5[kg] is sliding 11[m] down a frictionless inclined plane, inclination 37 degrees. It then hits a spring with K=800 [N/m] spring constant. How many meters would the spring be compressed?

10. Instantaneous Power
The instantaneous power is the limiting value of the average power as Dt approaches zero
This can also be written as

11. Units of Power The SI unit of power is called the watt
1 watt = 1 joule / second = 1 kg . m2 / s2
A unit of power in the US Customary system is horsepower
1 hp = 746 W
Units of power can also be used to express units of work or energy
1 kWh = (1000 W)(3600 s) = 3.6 x106 J

12. Example
A 50.0 kg marathon runner runs up the stairs to the top of Chicago’s 443-m-tall Sears Tower, the tallest building in the United States. To lift herself to the top in 15 minutes, what must be her average power output in watts? In kilowatts? In horsepower?