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Kinetic Energy

Definition 1: Kinetic Energy

Kinetic energy is the energy an object has due to its motion.

Kinetic energy is the energy an object has because of its motion. This means that any moving object has kinetic energy. The faster it moves, the more kinetic energy it has. Kinetic energy (KEKE) is therefore dependent on the velocity of the object. The mass of the object also plays a role. A truck of 2 000kg2 000kg, moving at 100km·hr-1100km·hr-1, will have more kinetic energy than a car of 500kg500kg, also moving at 100km·hr-1100km·hr-1. Kinetic energy is defined as:

K E = 1 2 m v 2 K E = 1 2 m v 2
(1)

Consider the 1kg1kg suitcase on the cupboard that was discussed earlier. When the suitcase falls, it will gain velocity (fall faster), until it reaches the ground with a maximum velocity. The suitcase will not have any kinetic energy when it is on top of the cupboard because it is not moving. Once it starts to fall it will gain kinetic energy, because it gains velocity. Its kinetic energy will increase until it is a maximum when the suitcase reaches the ground.

Figure 1
Figure 1 (PG10C3_008.png)

Exercise 1: Calculation of Kinetic Energy

A 1kg1kg brick falls off a 4m4m high roof. It reaches the ground with a velocity of 8,85m·s-18,85m·s-1. What is the kinetic energy of the brick when it starts to fall and when it reaches the ground?

Solution

  1. Step 1. Analyse the question to determine what information is provided :
    • The mass of the rock m=1kgm=1kg
    • The velocity of the rock at the bottom vbottom=8,85m·vbottom=8,85m·s-1-1

    These are both in the correct units so we do not have to worry about unit conversions.

  2. Step 2. Analyse the question to determine what is being asked :

    We are asked to find the kinetic energy of the brick at the top and the bottom. From the definition we know that to work out KEKE, we need to know the mass and the velocity of the object and we are given both of these values.

  3. Step 3. Calculate the kinetic energy at the top :

    Since the brick is not moving at the top, its kinetic energy is zero.

  4. Step 4. Substitute and calculate the kinetic energy :
    K E = 1 2 m v 2 = 1 2 ( 1 kg ) ( 8 , 85 m · s - 1 ) 2 = 39 , 2 J K E = 1 2 m v 2 = 1 2 ( 1 kg ) ( 8 , 85 m · s - 1 ) 2 = 39 , 2 J
    (2)

Checking units

According to the equation for kinetic energy, the unit should be kg·m2·s-2kg·m2·s-2. We can prove that this unit is equal to the joule, the unit for energy.

( kg ) ( m · s - 1 ) 2 = ( kg · m · s - 2 ) · m = N · m ( because Force ( N ) = mass ( kg ) × acceleration ( m · s - 2 ) ) = J ( Work ( J ) = Force ( N ) × distance ( m ) ) ( kg ) ( m · s - 1 ) 2 = ( kg · m · s - 2 ) · m = N · m ( because Force ( N ) = mass ( kg ) × acceleration ( m · s - 2 ) ) = J ( Work ( J ) = Force ( N ) × distance ( m ) )
(3)

We can do the same to prove that the unit for potential energy is equal to the joule:

( kg ) ( m · s - 2 ) ( m ) = N · m = J ( kg ) ( m · s - 2 ) ( m ) = N · m = J
(4)

Exercise 2: Mixing Units & Energy Calculations

A bullet, having a mass of 150g150g, is shot with a muzzle velocity of 960 m·s-1960m·s-1. Calculate its kinetic energy.

Solution
  1. Step 1. Analyse the question to determine what information is provided :
    • We are given the mass of the bullet m=150gm=150g. This is not the unit we want mass to be in. We need to convert to kg.
      Mass in grams ÷1000= Mass in kg 150g÷1000=0,150 kg Mass in grams ÷1000= Mass in kg 150g÷1000=0,150 kg
      (5)
    • We are given the initial velocity with which the bullet leaves the barrel, called the muzzle velocity, and it is v=960m·s-1v=960m·s-1.
  2. Step 2. Analyse the question to determine what is being asked :
    • We are asked to find the kinetic energy.
  3. Step 3. Substitute and calculate :

    We just substitute the mass and velocity (which are known) into the equation for kinetic energy:

    K E = 1 2 m v 2 = 1 2 ( 0 , 150 ) ( 960 ) 2 = 69 120 J K E = 1 2 m v 2 = 1 2 ( 0 , 150 ) ( 960 ) 2 = 69 120 J
    (6)

Kinetic Energy

  1. Describe the relationship between an object's kinetic energy and its:
    1. mass and
    2. velocity
    Click here for the solution
  2. A stone with a mass of 100g100g is thrown up into the air. It has an initial velocity of 3m·s-13m·s-1. Calculate its kinetic energy
    1. as it leaves the thrower's hand.
    2. when it reaches its turning point.
    Click here for the solution
  3. A car with a mass of 700kg700kg is travelling at a constant velocity of 100km·hr-1100km·hr-1. Calculate the kinetic energy of the car.
    Click here for the solution

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