Peoples Physics Concepts

http://www.ck12.org Chapter 8. Energy Conservation

8.1 Potential Energy

• Describe potential energy and how to calculate it.

Learn what potential energy is and how to calculate the potential energy of gravity and also that of a spring.

Key Equations

Gravitational potential energy

Ug=mgh







h height above the ground in meters(m)

g acceleration due to gravity, 9.8 m/s^2

Ug Potential energy of gravity (in Joules; 1 J=1kg m^2 /s^2 )

Spring potential energy

Us p=^12 k∆x^2







k spring constant measured in Newtons(N) per meters(m)

x amount spring is displaced from resting position

Us p potential energy of a spring (in Joules; 1 J=1kg m^2 /s^2 )

Guidance

Example 1

A 2 kg block of wood is suspended 5m above a spring of spring constant 3000 N/m. When the block is dropped on

the spring, how far will the spring be compressed from it’s equilibrium position.

Solution

We can solve for the distance the spring will be compressed using conservation of energy. In this problem, the

gravitational potential energy of the block will be turned into spring potential energy.

Ug=Us p start with by setting the gravitational potential energy equal to the spring potential energy

mgh=

1

2

k∆x^2 substitute the equations for gravitational and spring potential energy

∆x=

√

2 mgh

k

solve for∆x

∆x=

√

2 ∗2 kg∗ 9 .8 m/s^2 ∗5 m

3000 N/m

plug in the known values

∆x=.26 m