Formula of Kinetic EnergyKinetic energy refers to a type of energy that an object or body possesses by virtue of its motion. It is possessed by every particle performing any kind of motion. Kinetic energy is a property of a moving body or object that does not depend on motion only, but it also depends upon the body's mass. Mechanical energy can be divided into two different types, the first one is Kinetic energy, and the second one is potential energy. Potential energy refers to a type of energy that an object or body possessed by virtue of its position. For example, when an object is a free fall, the object possesses kinetic energy. Kinetic energy can be due to rotation, translation, and vibration. We can calculate KE using the mass and velocity of that body. In this article, we will discuss the formula to calculate the kinetic energy with certain examples. Method 1:Understanding Kinetic EnergyBy knowing the Formula The formula using for calculating the Kinetic energy is given below KE = ½ mv^{2} Where m = mass of an object or body. v = velocity of an object or body. Let's understand what is the mass and what is the velocity of an object. Mass: Mass of an object or body refers to how much matter is in the object. It is denoted by m. Unit of mass is the joule. Velocity: The velocity of an object refers to the rate at which the object changes its position. It is denoted by v. Unit of velocity is m/s. Calculate the mass of an object: When we solve a problem where the mass is not given, then first, you need to calculate the mass to proceed. This can be done by obtaining the mass in kg. Find the velocity of an object: You often face the problem while solving any problem, it does not give you the velocity of an object, but distance and time are given. Here, you need to calculate the velocity by applying the given formula. Velocity = Distance/time = d/t Example 1: If an object travels a distance of 8 meters in 2 sec, find the velocity of an object? Solution: Given, Distance = 8 meter Time = 2 sec We know that, V = distance/ time = 8/2 = 4 m/sec Example 2: If an object travels a distance of 10 meters in 5 sec, find the velocity of an object? Solution: Given, Distance = 10 meter Time = 5 sec We know that, V = distance/ time = 10/5 = 2 m/sec Method 2Finding the Kinetic EnergyWrite the equation: The formula used to calculate the Kinetic energy is given below. KE = ½ mv^{2} Where m = mass of an object or body. v = velocity of an object or body. The value of KE should always be in joules J, which is the standard unit of measurement of KE. Put the value of mass and velocity. To calculate the KE, you need to put the value of mass and velocity in the formula. If the value of mass and velocity are not given in the questions, you need to calculate it. Example 1: Find the KE of an 80 kg men running with a velocity of 8 m/s. Solution: Given; Mass = 80 kg Velocity = 8 m/s We know that, KE = ½ mv^{2} KE = ½ × 80 × 8^{2} ^{= }½ × 80 × 64 = 40 × 64 = 256 J Example 2: Find the KE of a 120 kg man running with a velocity of 10 m/s. Solution: Given; Mass = 120 kg Velocity = 10 m/s We know that, KE = ½ mv^{2} KE = ½ × 120 × 10^{2} = ½ × 120 × 100 = 60× 100 = 6000 J Using KE calculate velocity or Mass The formula using for calculating the Kinetic energy is given below KE = ½ mv^{2} Where, m = mass of an object or body v = velocity of an object or body. Put the Unknown Variables: In some questions, you have the value of KE and mass. In that case, you need to calculate the value of the velocity. Let's understand this concept with the help of an example Example 1: What is the velocity of a body with a mass of 50 kg, and the value of kinetic energy is 2500 J? Solution: Given; mass = 50 kg Kinetic Energy = 2500 J We know that KE = ½ mv^{2} 2500 = ½ × 50 × v^{2} v^{2} = 2500/25 v^{2 }= 100 v = 10 Example 2: What is the velocity of a body with a mass of 60 kg and the value of kinetic energy is 480 J? Solution: Given; mass = 60 kg Kinetic Energy = 480 J We know that KE = ½ mv^{2} 480 = ½ × 60 × v^{2} v^{2} = 480/30 v^{2} = 16 v = √16 = 4 Let's understand this concept with the help of an example Suppose you have the value of KE and velocity. In that case, you need to find the value of the mass. Example 1: Find the mass of an object with a kinetic energy of 500 J and a velocity of 10 m/s? Solution: Given; Kinetic energy = 500 J Velocity = 10 m/s We know that KE = ½ mv^{2} 500 = ½ × m ×10 ^{2} 500 = ½ × m ×100 500 = 50 × m m = 10 kg Example 2: Find the mass of an object with a kinetic energy of 600 J and a velocity of 20 m/s? Solution: Given; Kinetic energy = 600 J Velocity = 20 m/s We know that KE = ½ mv^{2} 600 = ½ × m ×20 ^{2} 500 = ½ × m ×400 500 = 200 × m m = 2.5 kg Questions based on kinetic energyQuestion 1: If a football has a mass of 3 kg, travels with a speed of 12 m/s, calculate the kinetic energy possessed by it. Solution: Given; Mass = 3 kg Velocity = 12 m/s We know that, Kinetic Energy = ½ mv^{2} KE = ½ ×3× (12)^{2} ^{= }½ ×3× 144 = 216 J Question 2: If a basketball has a mass of 4 kg, travels with a speed of 16 m/s, calculate the kinetic energy possessed by it. Solution: Given; Mass = 4 kg Velocity = 16 m/s We know that, Kinetic Energy = ½ mv^{2} KE = ½ ×4× (16)^{2} ^{= }½ ×4× 256 = 512 J Question 3: If a 12 kg object was traveling at a speed of 120 m/s. Now, this mass transfers all its energy to a mass of 24 k. What will be the velocity of the 24 kg mass after being hit by it? Solution: We know that, KE = ½ mv^{2} First, we will calculate the KE of the heavier object Given, M = 12 kg and v = 120 m/s We know that, KE = ½ mv^{2} = ½ × 12 × (120)^{2} = ½ × 12 × 14400 = 86400 J Now, this energy is transferred to another ball Given; Mass = 24 Kg Velocity =? We have calculated the value of kinetic energy KE = 86400 So, We know that, KE = ½ mv^{2} 86400 = ½ (24) v^{2} v^{2 }= 86400/12 = 7200 v = 60 m/s Question 4: If an 8 kg object was traveling at a speed of 80 m/s. Now, this mass transfers all its energy to a mass of 16 k. What will be the velocity of the 16 kg mass after being hit by it? Solution: We know that, KE = ½ mv^{2} First, we will calculate the KE of the heavier object Given, M = 8 kg and v = 80 m/s We know that, KE = ½ mv^{2} = ½ × 8 × (80)^{2} = ½ × 8 × 6400 = 25600 J Now, this energy is transferred to another ball Given; Mass = 16 Kg Velocity =? We have calculated the value of kinetic energy KE = 25600 So, We know that, KE = ½ mv^{2} 25600 = ½ (16) v^{2} v^{2 }= 25600/16 = 16 v = 4 m/s
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