4.06-4.07 KE and GPE

Matthew just threw a 0.15 kg ball straight up in the air. 1) What is the weight of the ball? 2) If the ball reaches a height of 9.0 m, what is its gravitational potential energy at this height? 3) What will happen to the gravitational potential energy of the ball as it falls? 4) What will happen to the kinetic energy of the ball as it falls?

1) m = 0.15 kg g = 9.8 m/s^2 W = ? W = mg W = (0.15 kg)( 9.8 m/s^2) W = 1.47 N W = 1.5 N 2) m = 0.15 kg g = 9.8 m/s^2 h = 9.0 m GPE = mgh GPE = (0.15 kg)( 9.8 m/s^2)( 9.0 m) GPE = 13.23 J GPE = 13 J 3) It decreases because there is a decrease in its height above the base level (in this case the ground). 4) It increases because as it experiences a decrease in height above base level, it has a gain in its velocity.

Potential Energy

An object can store energy due to its position or state of strain. This energy that is stored and held in readiness is called *potential energy*. The name gives the idea that the energy is in a stored state and has the potential to do work. We want to focus our study on potential energy due to the elevated position of an object. This energy is called *gravitational potential energy (GPE)*. The gravitational potential energy of an object depends on the mass (m) and height (h) of the object, as well as, the value of gravitational acceleration (g). The equation that relates these values is: *GPE = mgh*. We have already studied that the weight of an object is the product of the mass and the gravitational acceleration value: *W = mg*. Therefore, we can combine the two equations to yield: *GPE = Wh*

In your own words, explain how the potential energy of an object could be increased.

By changing the position or arrangement of the object, the potential energy can be increased or decreased. If an object is lifted higher within a gravitational field, it will have an increase in gravitational potential energy.

In your own words, what is the definition of "kinetic energy"?

Energy associated with motion; the work that an object can do because of its motion

What is the first thing that comes to your mind when you hear the term "kinetic energy"?

Many students think of the word kinetic in terms of motion, active, dynamic, energizing; therefore, kinetic energy would be "energy of motion."

Give an example of an object with kinetic energy.

Moving cars, trucks, and gas molecules would be examples of objects with kinetic energy.

If an object is moving, it has energy of motion. This energy that a moving object possesses is called *kinetic energy (KE)*. The kinetic energy of an object depends on the mass of the object, as well as, its speed. The equation that relates these values is *KE = 1/2mv^2*.

Notice that the Joule is a derived unit. 1 Joule = 1 (kg)(m/s)^2 = (kg)(m^2/s^2) In order for the kinetic energy to be expressed in Joules, the mass must be expressed in kilograms (kg) and the speed must be expressed in meters per second (m/s), which is then squared in the formula.

Consider the following situations: 1) A 2.5 kg physics book is resting on the edge of a table 1.1 m above the floor. 2) A 10.0 kg backpack is on the floor beside the door. In which situation (1 or 2) is the potential energy greater? Explain your choice.

The correct answer is 1 because the GPE is greater due to the position of the book above the earth.

Consider the following situations: 1) An 8000.0 kg train car is slowly coasting on a level track at a speed of 0.5 m/s. 2) Newton, a 20.0 kg greyhound, is racing down the straight part of a track at a speed of 12 m/s. In which situation (1 or 2) is the kinetic energy greater? Explain your choice.

The correct answer is 2. The KE for part A is 1000 J, and the KE for part B is 1440 J. Although the train has an extremely large mass compared to the greyhound, its speed is much smaller.

In your own words, explain how the kinetic energy of an object could be increased.

The kinetic energy of an object is given by the equation mv^2/2. You can increase the kinetic energy of an object by increasing either the mass of the object or its speed.

The SI unit for energy is the Joule.

The name for this unit was selected to honor the great scientist James Prescott Joule. The symbol for the Joule is "J."

What is the first thing that comes to your mind when you hear the term "potential energy"?

The word potential means "capable" of development into actuality or existing in possibility. Potential energy is energy that a piece of matter has because of its position or because of the arrangement of parts.

In your own words, what is the definition of "potential energy"?

The work an object can do because of its position or state is a good definition for the term "potential energy."

Give an example of an object with potential energy.

There are many examples of objects with potential energy. The work an object at a height can do in falling is its gravitational potential energy. The energy "stored" due to the elasticity of an object is called elastic potential energy. Books on a shelf and spring doors all have potential energy.

Sample Potential Energy Problem: Tom is holding a 2.10 kilogram physics book at a position 1.20 meters above the ground. What is the gravitational potential energy of the book?

m = 2.10 kg g = 9.80 m/s^2 h = 1.20 m GPE = ? GPE = mgh GPE = (2.1 kg)(9.8 m/s^2)(1.2 m) GPE = 24.7 (kg)(m/s^2)(m) GPE =24.7 (kg)(m^2/s^2) GPE = 24.7 J

Sample Kinetic Energy Problem: Almost every weekend, Ellen is out on the lake waterskiing. If Ellen's mass is 52.5 kilograms, and she is skiing across the lake at a speed of 12.6 m/s, what is her kinetic energy?

m = 52.5 kg v = 12.6 m/s KE = ? KE = 1/2mv^2 KE = (0.5)(52.5 kg)(12.6 m/s)^2 KE = 4167 J KE = 4.17 E3 J

Christy just got a new car for her 16th birthday. If she is traveling through town at a constant speed of 10.0 m/s, and the kinetic energy of the car is 5.18 E 4 J, what is the mass of the car and contents?

v = 10.0 m/s m = ? KE = 51800 J KE = mv^2/2 m = 2KE/ v^2 m = [(2)(51800 J)]/ (10.0 m/s)^2 m = 1036 kg m = 1040 kg

Evan is a championship runner of the school's track team. During one of his trials, his speed was measured at 10.1 m/s. Find Evan's kinetic energy during that trial if his mass is 58.6 kg.

v = 10.1 m/s m = 58.6 kg KE = ? KE = mv^2/2 KE = [(58.6 kg )(10.1 m/s)^2]/2 KE = 2988.893 KE = 2.99 E 3 J