We are given the muzzle velocity which is just how fast the bullet leaves the barrel and it is v = 960 m/s . Step 2 : Analyse the question to determine what is being asked • We are asked to find the kinetic energy. Step 3 : Substitute and calculate We just substitute the mass and velocity (which are known) into the equation for E k : E k = 1 2 mv 2 = 1 2 (150 kg )(960 m s ) 2 = 69 120 kgm 2 s 2 = 69 120 J 147
Potential Energy If you lift an object you have to do work on it. This means that energy is transferred to the object. But where is this energy? This energy is stored in the object and is called potential energy . The reason it is called potential energy is because if we let go of the object it would move. Definition: Potential energy is the energy an object has due to its position or state. As an object raised above the ground falls, its potential energy is released and transformed into kinetic energy. The further it falls the faster it moves as more of the stored potential energy is transferred into kinetic energy. Remember, energy is never created nor destroyed, but merely transformed from one type to another. In this case potential energy is lost but an equal amount of kinetic energy is gained. In the example of a falling mass the potential energy is known as gravitational potential energy as it is the gravitational force exerted by the earth which causes the mass to accelerate towards the ground. The gravitational field of the earth is what does the work in this case. Another example is a rubber-band. In order to stretch a rubber-band we have to do work on it. This means we transfer energy to the rubber-band and it gains potential energy. This potential energy is called elastic potential energy . Once released, the rubber-band begins to move and elastic potential energy is transferred into kinetic energy. Gravitational Potential Energy As we have mentioned, when lifting an object it gains gravitational potential energy. One is free to define any level as corresponding to zero gravitational potential energy. Objects above this level then possess positive potential energy, while those below it have negative potential energy. To avoid negative numbers in a problem, always choose the lowest level as the zero potential mark. The change in gravitational potential energy of an object is given by: Δ E P = mg Δ h Δ E P : Change in gravitational potential energy ( J ) m : mass of object ( kg ) g : acceleration due to gravity ( m.s - 2 ) Δ h : change in height ( m ) When an object is lifted it gains gravitational potential energy, while it loses gravitational potential energy as it falls. Worked Example 45 Gravitational potential energy 148
Question: How much potential energy does a brick with a mass of 1 kg gain if it is lifted 4 m . Answer: Step 1 : Analyse the question to determine what information is provided • The mass of the brick is m = 1 kg • The height lifted is Δ h = 4 m These are in the correct units so we do not have to worry about unit conversions.
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