Kinetic Energyis the energy possessed by an object by virtue of its motion. Kinetic Energy is a consequence of the object’s velocity. Because of its motion, the object is capable of performing work, or transferring energy.
A bowling ball that is made to roll along the bowling lane possess kinetic energy. The kinetic energy of the bowling ball depends on two variables - its mass and its velocity. Kinetic energy is directly proportional to mass. A heavier object has more kinetic energy than a lighter one, granted both objects are moving at the same speed.
A heavier truck posses more kinetic energy than the smaller truck. The KE of the 5000 kg truck is 250,000 J at 10 m/s velocity while the 10,000 kg truck has a KE of 500,000 J
In terms of velocity, the faster the ball rolls, the greater is its kinetic energy. In fact, the relationship between kinetic energy and velocity is a direct square relationship. Kinetic energy is directly proportional to the square of the objects velocity. When an object's velocity is increased twice, the kinetic energy of the object increases four times. The acquired kinetic energy of the bowling ball makes it capable of performing work on the pins. As the massive, fast moving ball hits the pins, the pins are thrown from their position. The work performed by the ball on the pins can be computed byWork = Force x displacement.
Kinetic energy is measured in terms of SI unitjoule. The unit joule (symbol: J) is named in honor to the scientistJames Prescott Joulewho discovered the relationship between heat and work. Kinetic energy is computed using the formulaKE = 1/2 (mv2)which can also be written asKE = (mv2)/2.
As said, kinetic energy is directly proportional to mass. When comparing kinetic energies of two different objects with different masses but are moving at the same velocity, the more massive object has more kinetic energy than the less massive one.
Sample Problems:
Problem 1. A baseball has a mass of 0.15 kg. Calculate the kinetic energy of the baseball moving at 20 m/s.
Given: Mass = 0.15 kg Velocity = 20 m/s
Required: Kinetic Energy
Equation: KE = (mv2)/2
Solution: KE = [(0.15 kg) (20 m/s)2] / 2 KE = [(0.15 kg) (400 m2/s2)] / 2 KE = (60 kg ・m2/s2) / 2 KE = 30 kg ・m2/s2 KE = 30 joules
Problem 2.What is the KE of the baseball (mass = 0.15 kg) if its velocity is 40 m/s?
Given: Mass = 0.15 kg Velocity = 40 m/s
Required: Kinetic Energy
Equation: KE = (mv2)/2
Solution: KE = [(0.15 kg) (40 m/s)2] / 2 KE = [(0.15 kg) (1600 m2/s2)] / 2 KE = (240 kg ・m2/s2) / 2 KE = 120 kg ・m2/s2 KE = 120 joules
Notice that as the velocity of the baseball is doubled, its kinetic energy is increased four times (from 30 joules to 120 joules!)
Problem 3. An object has a kinetic energy of 35 joules. If the velocity of the object is 2 m/s, what is the mass of the object?
Given: Kinetic Energy = 35 J Velocity = 2 m/s
Required: Mass
Equation: KE = (mv2)/2 m = 2 KE / v2
Solution: m = (2 x 35 J) / (2 m/s)2 m = 70 J / 4 m2/s2 m = 70 kg m2/s2 / 4 m2/s2 m = 17.5 kg
Problem 4. What is the velocity of a ball with mass of 0.5 kg and a kinetic energy of 30 J?
Given: Kinetic Energy = 30 J Mass = 0.5 kg
Required: Velocity
Equation: KE = (mv2)/2 v = √(2KE/m) v = √[2 (30 J )] / 0.5 kg) v = √ 60J / 0.5 kg) v = √ 60 kg m2/s2 / 0.5 kg) v = √ 120 m2/s2 v = √ 120 m2/s2
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