Potential Energy Kinetic

Energy

Gravitational Potential

Elastic Potential

Chemical Potential

All Energy

The basic motion of energy is stored work. A tankful of gas, a heavy truck moving at speed, and a charged automobile battery all possess energy. §  The energy associated with a mass in motion is called kinetic

energy

§  Energy an object possesses due to its condition or position is called potential energy.

Gravitational Potential Energy: Energy an object possesses because of its position in a gravitational field (height) Formula PE = m·g·h m = mass (kg) g = constant (9.81 m/s2 or 32 ft/s2) h = vertical displacement height (m or ft)

Units: Joules (J) or Ft-lbs

Example 1: A crate of mass 5,000 kg is raised slowly to a height of 12 m above its original position. What is the potential energy at the height of 12m? PE = m·g·h PE = 5000 kg x 9.81 m/s2 x 12 m PE = 588,600 J

Elastic Potential Energy Potential energy due to deformation (stretching) of an elastic object. 1.  Drawn bow and arrow 2.  Stretched or compressed spring 3.  Stretched rubber band

Hooke's Law gives the relationship between the force applied to an upstretched spring and the amount the spring is stretched.

•  Every spring has an elastic limit.

•  If the spring is stretched within its elastic limit, it “springs” back to its “rest point”.

•  If a spring is stretched beyond its elastic limit, it becomes deformed.

•  As illustrated below, the distance a spring is stretched is called the “elongation”.

•  Robert Hooke was the first to discover that the spring force is directly proportional to the elongation.

•  This relationship is known as Hooke’s Law.

Hooke’s Law formula: F = k·x F = the spring force (N) k = the force or spring constant (N/m) ~ different for each spring x = the distance or elongation of the spring from rest or equilibrium position (m)

•  The force constant or spring constant is the force required to stretch a given object.

•  The force or spring constant is different for different springs and depends upon the type of material the spring is made of as well as the thickness of the spring coil.

•  The greater the value of the force or spring constant, the “stiffer” the spring.

Example #2

100 N/m

Example #3

(0.3, 1)

(0.67, 3)

(1.5, 6) (1.3, 5) (1.0, 4)

F = k·x 6 N = k ·1.5m K = 4 N/m

Example #4 A 10 N force compresses a spring 0.25 meters from its equilibrium position. Calculate the spring constant of this spring.

40 N/m

Example #5 A coiled spring is stretched 0.05 m by a weight of 0.50 N hung from one end. a.  How far will the spring stretch if a 1.0 N weight replaces the

0.50 N weight? b.   What weight will stretch the spring a distance of 0.03 m?

1.  0.1 m 2.  0.3 N

Elastic PE Formula: PE = ½ k (Δx)2

k = Force constant (N/m) Δx = distance the object has stretched or been compressed from rest position(m) Units: Joules (J) or Ft-lbs

Example #6 A spring with a spring constant of 4 N/m is compressed by a force of 1.2 N. What is the total elastic potential energy stored in this compressed spring?

0.18 J

Example #7 Jan's mountain bike has a spring with a force constant of 64 N/m in the front-wheel suspension. If it is compressed 0.17 m when she hit a bump, how much energy does the front spring now store?

PE = ½ k (∆x)2

PE = ½ (64 N/m)(0.17 m)2

PE = 0.925 J

Example #8 A spring has 1.1 J of potential energy and was compressed 0.2 m. What is its spring constant?

PE = ½ k (∆x)2

1.1 J = ½ k (0.2 m)2

k = 55 N/m

Chemical Potential Energy Potential energy stored within the chemical bonds of an object

•  Energy an object due to its motion

•  The ability or capacity of a moving object to move another object

•  Kinetic energy exists whenever an object which has mass is in motion with some velocity.

Kinetic Energy Formula: KE = ½ mv2 m = mass (kg) V = Velocity (m/s or ft/s) Units: Joules (J) or Ft-lbs

Example #5: What is the Kinetic Energy of a 1,000 kg car moving at 30 m/s?

KE = 450,000 J

Example #6: What is the Kinetic Energy of a 20,000 kg freight car moving at 25 m/s? KE = ½ mv2 KE = ½ (20,000) (25 m/s)2

KE = 6,250,000 J

Example #7: What is the Kinetic Energy of a 0.04 g BB traveling 200 m/s? KE = ½ mv2 KE = ½ (.00004 kg) (200 m/s)2

KE = 0.8 J

Example #8 Calculate the mass of a truck with 81,000 J of Kinetic Energy if its speed is 14 m/s.

KE = ½ mv2 81,000 J = ½ m (14 m/s)2

m = 826.53 kg