The kinetic energy of an object of mass, m moving with a velocity of 5 ms is 25 j. what will be its kinetic energy when its velocity is doubled? what will be its kinetic energy when its velocity is increased three times?

12 Thermodynamics • Introduction • 12.1 Zeroth Law of Thermodynamics: Thermal Equilibrium • 12.2 First law of Thermodynamics: Thermal Energy and Work • 12.3 Second Law of Thermodynamics: Entropy • 12.4 Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators • Key Terms • Section Summary • Key Equations • 22 The Atom • Introduction • 22.1 The Structure of the Atom • 22.2 Nuclear Forces and Radioactivity • 22.3 Half Life and Radiometric Dating • 22.4 Nuclear Fission and Fusion • 22.5 Medical Applications of Radioactivity: Diagnostic Imaging and Radiation • Key Terms • Section Summary • Key Equations • Teacher Support The learning objectives in this section will help your students master the following standards: • (6) Science concepts. The student knows that changes occur within a physical system and applies the laws of conservation of energy and momentum. The student is expected to: • (B) investigate examples of kinetic and potential energy and their transformations; • (D) demonstrate and apply the laws of conservation of energy and conservation of momentum in one dimension. In addition, the High School Physics Laboratory Manual addresses content in this section in the lab titled: Work and Energy, as well as the following standards: • (6) Science concepts. The student knows that changes occur within a physical system and applies the laws of conservation of energy and momentum. The student is expected to: • (B) investigate examples of kinetic and potential...

Kinetic energy, k = \(\frac)^2\) Initial kinetic energy k 1= 25J Initial velocity V 2= 5 ms -1 New kinetic Energy K 2= ? New velocity v 2= 3v 1= 3 × 5 = 10 ms -1 ∴ When velocity is increased three times its K.E. is 225 J.

Hint:We know that the kinetic energy is expressed as the energy which is due to the motion of any object. It depends on the mass and the velocity of the moving object. here, we will find the correlation between the velocity and the energy of an object and will find the mass of the body. Complete step by step answer: As the velocity is given as $5\,m$ $\Rightarrow K.E = 9 \times 25$ $\therefore K.E = 225\,J$

Step 1: Given data The kinetic energy of an object (K.E) = 25 J The velocity of the object (V) = 5 ms - 1 Mass of the object = m Step 2: Formula used K . E = 1 2 mv 2 For the mass of the object ⇒ K . E = 1 2 mv 2 ⇒ 25 = 1 2 × m × 5 2 ⇒ 50 = 25 m ⇒ m = 2 kg Step 3: Calculation Case 1: When velocity is doubled, then v = 10 ms - 1 m = 2 kg So ⇒ K . E = 1 2 mv 2 ⇒ K . E = 1 2 × 2 × 10 2 ⇒ K . E = 100 J So its kinetic energy is 100 J when its velocity is doubled. Case 2: When its velocity is increased three times, then v = 15 ms - 1 m = 2 kg So ⇒ K . E = 1 2 mv 2 ⇒ K . E = 1 2 × 2 × 15 2 ⇒ K . E = 225 J So its kinetic energy is 225 J when its velocity is increased three times.

Mass and weight are actually not the same thing in Physics, even though we sometimes use the words interchangeably in everyday life. Mass can be described as “how hard it is to move” something. Imagine you and an elephant are each on a skateboard. If we gave the same push to each of you, you would move a lot more than the elephant. That’s because you are less massive than an elephant. Weight is the force of gravity acting on an object. Because gravity can be stronger or weaker depending on what planet (or other object) you’re near, your weight changes too! If you went to the Moon, the force of gravity on you would be about one-sixth what it is on Earth. That means that even though your mass is the same on the Earth or Moon, you’d weigh much less on the Moon! We often measure an object’s mass by comparing how gravity (in the same location) acts on a known mass for comparison. If you see a balance-style scale, it’s measuring mass. Weight is measured like other forces. Many bathroom scales use springs to measure the force of gravity acting on the object on top of them. This means if you took a bathroom scale to the Moon, it would read one-sixth your weight on Earth. Does that help?

Step 1: Given data. Velocity, v = 5 m s - 1 Kinetic energy, k = 25 J Mass, m = ? Step 2: Calculate the mass. The mass of the body is calculated below: k = 1 2 mv 2 m = 2 k v 2 m = 2 × 25 5 2 m = 2 × 25 25 m = 2 k g Step 3: Calculate the kinetic energy when the velocity is doubled. New velocity, v 2 = 5 m s - 1 × 2 = 10 m s - 1 New kinetic energy, k 2 is calculated below: k 2 = 1 2 m v 2 2 k 2 = 1 2 × 2 k g × 10 m s - 1 2 k 2 = 1 2 × 2 × 100 k 2 = 100 J Step 4: Calculate the kinetic energy when the velocity is increased three times. New velocity, v 3 = 5 m s - 1 × 3 = 15 m s - 1 New kinetic energy, k 3 is calculated below: k 3 = 1 2 m v 3 2 k 2 = 1 2 × 2 k g × 15 m s - 1 2 k 2 = 1 2 × 2 × 225 k 2 = 225 J

If we want to accelerate an object, then we must apply a force. Applying a force requires us to do work. After work has been done, energy has been transferred to the object, and the object will be moving with a new constant speed. The energy transferred is known as kinetic energy, and it depends on the mass and speed achieved. Kinetic energy can be transferred between objects and transformed into other kinds of energy. For example, a flying squirrel might collide with a stationary chipmunk. Following the collision, some of the initial kinetic energy of the squirrel might have been transferred into the chipmunk or transformed to some other form of energy. To calculate kinetic energy, we follow the reasoning outlined above and begin by finding the work done, W W W W , by a force, F F F F , in a simple example. Consider a box of mass m m m m being pushed through a distance d d d d along a surface by a force parallel to that surface. As we learned earlier W = m ⋅ d ⋅ v f 2 − v i 2 2 d = m ⋅ v f 2 − v i 2 2 = 1 2 ⋅ m ⋅ v f 2 − 1 2 ⋅ m ⋅ v i 2 \begin W ​ = m ⋅ d ⋅ 2 d v f 2 ​ − v i 2 ​ ​ = m ⋅ 2 v f 2 ​ − v i 2 ​ ​ = 2 1 ​ ⋅ m ⋅ v f 2 ​ − 2 1 ​ ⋅ m ⋅ v i 2 ​ ​ • Kinetic energy depends on the velocity of the object squared. This means that when the velocity of an object doubles, its kinetic energy quadruples. A car traveling at 60 mph has four times the kinetic energy of an identical car traveling at 30 mph, and hence the potential for four times more death and destruction in the...

If we want to accelerate an object, then we must apply a force. Applying a force requires us to do work. After work has been done, energy has been transferred to the object, and the object will be moving with a new constant speed. The energy transferred is known as kinetic energy, and it depends on the mass and speed achieved. Kinetic energy can be transferred between objects and transformed into other kinds of energy. For example, a flying squirrel might collide with a stationary chipmunk. Following the collision, some of the initial kinetic energy of the squirrel might have been transferred into the chipmunk or transformed to some other form of energy. To calculate kinetic energy, we follow the reasoning outlined above and begin by finding the work done, W W W W , by a force, F F F F , in a simple example. Consider a box of mass m m m m being pushed through a distance d d d d along a surface by a force parallel to that surface. As we learned earlier W = m ⋅ d ⋅ v f 2 − v i 2 2 d = m ⋅ v f 2 − v i 2 2 = 1 2 ⋅ m ⋅ v f 2 − 1 2 ⋅ m ⋅ v i 2 \begin W ​ = m ⋅ d ⋅ 2 d v f 2 ​ − v i 2 ​ ​ = m ⋅ 2 v f 2 ​ − v i 2 ​ ​ = 2 1 ​ ⋅ m ⋅ v f 2 ​ − 2 1 ​ ⋅ m ⋅ v i 2 ​ ​ • Kinetic energy depends on the velocity of the object squared. This means that when the velocity of an object doubles, its kinetic energy quadruples. A car traveling at 60 mph has four times the kinetic energy of an identical car traveling at 30 mph, and hence the potential for four times more death and destruction in the...

Step 1: Given data. Velocity, v = 5 m s - 1 Kinetic energy, k = 25 J Mass, m = ? Step 2: Calculate the mass. The mass of the body is calculated below: k = 1 2 mv 2 m = 2 k v 2 m = 2 × 25 5 2 m = 2 × 25 25 m = 2 k g Step 3: Calculate the kinetic energy when the velocity is doubled. New velocity, v 2 = 5 m s - 1 × 2 = 10 m s - 1 New kinetic energy, k 2 is calculated below: k 2 = 1 2 m v 2 2 k 2 = 1 2 × 2 k g × 10 m s - 1 2 k 2 = 1 2 × 2 × 100 k 2 = 100 J Step 4: Calculate the kinetic energy when the velocity is increased three times. New velocity, v 3 = 5 m s - 1 × 3 = 15 m s - 1 New kinetic energy, k 3 is calculated below: k 3 = 1 2 m v 3 2 k 2 = 1 2 × 2 k g × 15 m s - 1 2 k 2 = 1 2 × 2 × 225 k 2 = 225 J

12 Thermodynamics • Introduction • 12.1 Zeroth Law of Thermodynamics: Thermal Equilibrium • 12.2 First law of Thermodynamics: Thermal Energy and Work • 12.3 Second Law of Thermodynamics: Entropy • 12.4 Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators • Key Terms • Section Summary • Key Equations • 22 The Atom • Introduction • 22.1 The Structure of the Atom • 22.2 Nuclear Forces and Radioactivity • 22.3 Half Life and Radiometric Dating • 22.4 Nuclear Fission and Fusion • 22.5 Medical Applications of Radioactivity: Diagnostic Imaging and Radiation • Key Terms • Section Summary • Key Equations • Teacher Support The learning objectives in this section will help your students master the following standards: • (6) Science concepts. The student knows that changes occur within a physical system and applies the laws of conservation of energy and momentum. The student is expected to: • (B) investigate examples of kinetic and potential energy and their transformations; • (D) demonstrate and apply the laws of conservation of energy and conservation of momentum in one dimension. In addition, the High School Physics Laboratory Manual addresses content in this section in the lab titled: Work and Energy, as well as the following standards: • (6) Science concepts. The student knows that changes occur within a physical system and applies the laws of conservation of energy and momentum. The student is expected to: • (B) investigate examples of kinetic and potential...