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Potential Energy Work Kinetic Energy

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**An object can store energy as the result of its position**

An object can store energy as the result of its position. For example, the heavy ball of a demolition machine is storing energy when it is held at an elevated position. This stored energy of position is referred to as potential energy.

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**Just like a drawn bow is able to store energy as the result of its position.**

When assuming its usual position (i.e., when not drawn), there is no energy stored in the bow. Yet when its position is altered from its usual equilibrium position, the bow is able to store energy by virtue of its position. This stored energy of position is referred to as potential energy. Potential energy is the stored energy of position possessed by an object.

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**Gravitational Potential Energy**

The two examples above illustrate the two forms of potential energy to be discussed in this course - gravitational potential energy and elastic potential energy. Gravitational potential energy is the energy stored in an object as the result of its vertical position or height. The energy is stored as the result of the gravitational attraction of the Earth for the object. The gravitational potential energy of the massive ball of a demolition machine is dependent on two variables - the mass of the ball and the height to which it is raised.

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There is a direct relation between gravitational potential energy and the mass of an object. More massive objects have greater gravitational potential energy. There is also a direct relation between gravitational potential energy and the height of an object. The higher that an object is elevated, the greater the gravitational potential energy. These relationships are expressed by the following equation: PEgrav = mass • g • height

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**Use this principle to determine the blanks in the following diagram**

Use this principle to determine the blanks in the following diagram. Knowing that the potential energy at the top of the tall platform is 50 J, what is the potential energy at the other positions shown on the stair steps and the incline?

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**A: PE = 40 J (since the same mass is elevated to 4/5-ths height of the top stair)**

B: PE = 30 J (since the same mass is elevated to 3/5-ths height of the top stair) C: PE = 20 J (since the same mass is elevated to 2/5-ths height of the top stair) D: PE = 10 J (since the same mass is elevated to 1/5-ths height of the top stair) E and F: PE = 0 J (since the same mass is at the same zero height position as shown for the bottom stair).

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PE going to KE

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QUIZ AGAIN

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1. A cart is loaded with a brick and pulled at constant speed along an inclined plane to the height of a seat-top. If the mass of the loaded cart is 3.0 kg and the height of the seat top is 0.45 meters, then what is the potential energy of the loaded cart at the height of the seat-top?

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2. If a force of 14.7 N is used to drag the loaded cart (from previous question) along the incline for a distance of 0.90 meters, then how much work is done on the loaded cart?

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Answer #1 PE = m*g*h PE = (3 kg ) * (9.8 m/s/s) * (0.45 m) PE = 13.2 J

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Answer #2 W = F * d * cos Theta W = 14.7 N * 0.9 m * cos (0 degrees) W = 13.2 J

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In the following descriptions, the only forces doing work upon the objects are internal forces - gravitational and spring forces. Thus, energy is transformed from KE to PE (or vice versa) while the total amount of mechanical energy is conserved. Read each description and indicate whether energy is transformed from KE to PE or from PE to KE.

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**A ball falls from a height of 2 meters in the absence of air resistance.**

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PE to KE The ball is losing height (falling) and gaining speed. Thus, the internal or conservative force (gravity) transforms the energy from PE (height) to KE (speed).

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**A skier glides from location A to location B across a friction free ice.**

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PE to KE The skier is losing height (the final location is lower than the starting location) and gaining speed (the skier is faster at B than at A). Thus, the internal force or conservative (gravity) transforms the energy from PE (height) to KE (speed).

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**A baseball is traveling upward towards a man in the bleachers.**

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KE to PE The ball is gaining height (rising) and losing speed (slowing down). Thus, the internal or conservative force (gravity) transforms the energy from KE (speed) to PE (height).

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**A bungee cord begins to exert an upward force upon a falling bungee jumper.**

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KE to PE The jumper is losing speed (slowing down) and the bunjee cord is stretching. Thus, the internal or conservative force (spring) transforms the energy from KE (speed) to PE (a stretched "spring"). One might also argue that the gravitational PE is decreasing due to the loss of height.

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**The spring of a dart gun exerts a force on a dart as it is launched from an initial rest position.**

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PE to KE The spring changes from a compressed state to a relaxed state and the dart starts moving. So, the internal or conservative force (spring) transforms the energy from PE (a compressed spring) to KE (speed).

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Kinetic Energy The word 'kinetic' is derived from the modern Greek word, 'kinesis', meaning 'to move'. In physics, if an object has energy then we say it has the ability to work (more on work later). Kinetic energy is the energy of motion and it follows that any object with a velocity or which is moving is producing kinetic energy.

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**The faster the body moves the more kinetic energy is produced**

The faster the body moves the more kinetic energy is produced. The greater the mass and speed of an object the more kinetic energy there will be. As a car accelerates down a hill, its velocity increases and so does the kinetic energy it is producing. The potential energy posseses by the car at the top of the hill is being changed into kinetic energy.

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**Kinetic energy is often defined informally as energy of motion**

Kinetic energy is often defined informally as energy of motion. It is better defined as the work it would take to get an object of mass, m, moving with velocity, v, and is given by the formula: Ek = ½mv2

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Ek = ½mv2 Where: Ek = kinetic energy in joules (J), m = mass of the object in kilograms (kg), v = the velocity of the object in metres per second (ms-1). The net work done on an object is equal to the change in its kinetic or potential energy.

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Energy and work Sections 12, 13, 14 and 15

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