Question 1 Write detailed answers.

(a) Explain the difference between potential energy and kinetic energy.
Answer: Potential energy is energy stored due to an object’s position or arrangement. For example, a ball that is held up in the air has potential energy because of its position. If the ball is released, it will fall and the potential energy will be converted into kinetic energy.

• Kinetic energy is energy that is possessed by an object due to its motion. For example, a moving car has kinetic energy. The faster the car moves, the greater its kinetic energy.

The main difference between potential energy and kinetic energy is that potential energy is stored energy, while kinetic energy is energy in motion. Potential energy can be converted into kinetic energy, and vice versa.

Here are some other ways to think about the difference between potential energy and kinetic energy:

• Potential energy is like a reservoir of energy, while kinetic energy is like the water that is flowing out of the reservoir.
• Potential energy is like a wound upspring, while kinetic energy is like the spring that is unwinding.
• Potential energy is like a stretched rubber band, while kinetic energy is like the rubber band that is snapping back.

(b)Derive the formula for the kinetic energy of an object of mass m, moving with velocity v.
Answer: The derivation of the formula for the kinetic energy of an object of mass m, moving with velocity v.

Let’s imagine a car that is moving. The car has kinetic energy because it is moving. The faster the car is moving, the greater its kinetic energy.

We can measure kinetic energy in joules (J). A joule is a unit of energy equal to the work done by a force of 1 Newton acting through a distance of 1 meter.

Now, let’s think about how we can calculate kinetic energy. We know that kinetic energy is related to the mass of the object and its velocity. The greater the mass of the object, the greater its kinetic energy. The faster the object is moving, the greater its kinetic energy.

We can express this mathematically as follows:

Kinetic energy = (1/2) mv^2

where:

• m is the mass of the object (in kilograms)
• v is the velocity of the object (in meters per second)

The 1/2 in the formula is a constant of proportionality. It doesn’t have any physical meaning, but it helps us get the units right.

So, this is the formula for the kinetic energy of an object of mass m, moving with velocity v. It is a simple formula, but it is very important in physics. It can be used to calculate the kinetic energy of anything that is moving, from a baseball to a car to a planet.

 

(c)Prove that the kinetic energy of a freely falling object reaching the ground is nothing but the transformation of its initial potential energy.

Answer. Let’s say we have an object of mass m that is dropped from a height h. The initial potential energy of the object is:

PE = mg

where g is the acceleration due to gravity.

As the object falls, its potential energy decreases, and its kinetic energy increases. When the object reaches the ground, its potential energy is zero and its kinetic energy is equal to its initial potential energy, mgh.

We can prove this mathematically by using the law of conservation of energy. The law of conservation of energy states that the total energy of an isolated system remains constant. In this case, the isolated system is the object.

The total energy of the object at the beginning is equal to its potential energy, mgh. The total energy of the object at the end is equal to its kinetic energy, KE.

Therefore, we have the following equation:

mgh = KE

where KE is the kinetic energy of the object at the end.

The kinetic energy of the object is equal to 1/2 mv^2, where v is the velocity of the object at the end.

Solving for v, we get:

v = sqrt(2gh)

This means that the velocity of the object at the end is equal to the square root of 2gh.

In numerical terms, let’s say the object has a mass of 1 kg and is dropped from a height of 10 m. The initial potential energy of the object is:

PE = mgh = (1 kg) (9.8 m/s^2) (10 m) = 98 J

When the object reaches the ground, its kinetic energy is equal to 98 J. The velocity of the object at the ground is:

v = sqrt(2gh) = sqrt (2) (9.8 m/s^2) (10 m) = 14 m/s

Therefore, the kinetic energy of the object reaching the ground is nothing but the transformation of its initial potential energy.

(d)Determine the amount of work done when an object is displaced at an angle of 300 concerning the direction of the applied force.

Answer. The force F applied to the weight W is resolved into two components:

• Fcos(θ), which is parallel to the surface, and does not work because it has no displacement.
• Fsin(θ), which is perpendicular to the surface, and does work because it has a displacement.

The work done by the force F is:

Work = Fsin(θ) x s

where:

• F is the force (in newtons)
• θ is the angle between the force and the displacement (in degrees)
• s is the displacement (in meters)

 

(e)If an object has 0 momentum, does it have kinetic energy? Explain your answer.
Answer: No, an object with zero momentum does not have kinetic energy. Kinetic energy is the energy of motion, and momentum is the product of mass and velocity. If an object has zero momentum, it either has zero mass zero velocity, or both. In either case, it cannot have kinetic energy.

(f)Why is the work done on an object moving with uniform circular motion zero?

Answer: Imagine you are riding a bike in a circle. The force that keeps you moving in the circle is called the centripetal force. This force is always directed towards the center of the circle.

The displacement of your bike is always tangent to the circle.

Work is done when a force acts on an object and the object moves in the direction of the force. In the case of your bike, the centripetal force is acting on you, but you are not moving in the direction of the force. You are moving tangent to the circle.

The work done by a force is equal to the force multiplied by the displacement, multiplied by the cosine of the angle between the force and the displacement. In the case of your bike, the angle between the centripetal force and your displacement is 90 degrees. The cosine of 90 degrees is zero, so the work done is zero.

This is why the work done on an object moving with uniform circular motion is zero. The force is always perpendicular to the displacement, so the cosine of the angle between the force and the displacement is zero, and the work done is zero

Question2.Choose one or more correct alternatives.

(a)For work to be performed, energy must be ….

(i) transferred from one place to another

(ii) concentrated

(iii) transformed from one type to another

(iv) destroyed

Answer. For work to be performed, energy must be transferred from one place to another

(b)Joule is the unit of …

(i) force

(ii) work

(iii) power

(iv) energy

Answer. Joule is the unit of work and energy

(c)Which of the forces involved in dragging a heavy object on a smooth, horizontal surface, have the same magnitude?

(i) The horizontal applied force

(ii) gravitational force

(iii) reaction force in the vertical direction

(iv) force of friction

Answer. gravitational force and reaction force in the vertical direction have the same magnitude

(d)Power is a measure of the …….

(i) the rapidity with which work is done

(ii) amount of energy required to perform the work

(iii) The slowness with which work is performed

(iv) length of time

Answer. Power is a measure of the rapidity with which work is done

(e)While dragging or lifting an object, negative work is done by

(i) The applied force

(ii) gravitational force

(iii) frictional force

(iv) Reaction force

Answer. While dragging or lifting an object, negative work is done by frictional force and gravitational force

Question3.Rewrite the following sentences using a proper alternative.

(a)The potential energy of your body is least when you are ….

(i) sitting on a chair

(ii) sitting on the ground

(iii) sleeping on the ground

(iv) standing on the ground

Answer: (iii) The potential energy of your body is least when you are sleeping on the ground

(b) the total energy of an object falling freely toward the ground …

(i) decreases

(ii) remains unchanged

(iii) increases

(iv) increases in the beginning and then decreases

Answer:(iii) The total energy of an object falling freely toward the ground increases

(c)If we increase the velocity of a car moving on a flat surface to four times its original speed, its potential energy ….

(i) will be twice its original energy

(ii) will not change

(iii) will be 4 times its original energy

(iv) will be 16 times its original energy.

Answer: If we increase the velocity of a car moving on a flat surface to four times its original speed, its potential energy will not change

(d)The work done on an object does not depend on ….

(i) displacement

(ii) applied force

(iii) initial velocity of the object

(iv) the angle between force and displacement.

Answer:(iii) The work done on an object does not depend on the initial velocity of the object

Question4.Study the following activity and answer the questions.

1. Take two aluminum channels of different lengths.
2. Place the lower ends of the channels on the floor and hold their upper ends at the same height.
   3. Now take two balls of the same size and weight and release them from the top end of the channels. They will roll down and cover the same distance.

Questions
1. At the moment of releasing the balls, which energy do the balls have?
2. As the balls roll down which energy is converted into which other form of energy?
3. Why do the balls cover the same distance on rolling down?
4. What is the form of the eventual total energy of the balls?
5. Which law related to energy does the above activity demonstrate? Explain.
Answer:

1. When a ball is released from a height, it has potential energy due to its position.

2. As the ball rolls down, the potential energy is converted into kinetic energy, which is the energy of motion. The ball will continue to roll until all of the potential energy has been converted into kinetic energy.

3. The distance that the ball rolls will depend on the amount of potential energy it has at the start. If two balls are released from the same height, they will roll the same distance, regardless of their mass or weight. This is because the amount of potential energy is the same for both balls.

4. The total energy of the ball is the sum of its potential energy and kinetic energy. This total energy is conserved as the ball rolls down. In other words, the amount of energy the ball has at the start is the same amount of energy it has at the end.

5.The law of conservation of energy states that energy cannot be created or destroyed, but can only be converted from one form to another. The activity of releasing a ball from a height is a demonstration of this law.

Question5.Solve the following examples.

(a)An electric pump has 2 kW power. How much water will the pump lift every minute to a height of 10 m? (Ans: 1224.5 kg)
Answer: The amount of water that a pump can lift is determined by its power, the height to which the water is being lifted, and the time it takes to lift the water.

In this case, the pump has a power of 2 kW. This means that it can do 2000 joules of work in one second. The height to which the water is being lifted is 10 meters. The time it takes to lift the water is one minute, which is 60 seconds.

To calculate the amount of water that the pump can lift, we use the following formula:

Power = Work / Timework = Force x Distancer = Mass x Gravity Mass = Volume x Density Volume = Weight / Density Weight = Mass x Gravity

Putting in the known values, we get:

2000 J = Work / 60 s Work = 12000 J Work = Force x Distance12000 J = Force x 10 m Force = 1200 N Force = Mass x Gravity1200 N = Mass x  9.81 m/s²Mass = 122.45 kg Volume = Weight / Density Volume = 122.45 kg / 1000 kg/m³Volume = 0.12245 m³

Therefore, the pump can lift 0.12245 cubic meters of water every minute to a height of 10 meters. This is equivalent to 1224.5 liters of water.

(b)If A 1200 W electric iron is used daily for 30 minutes, how much total electricity is consumed in April?

Answer.Let’s break down the problem into smaller steps.

• What does P stand for? P stands for power. Power is the rate at which work is done. It is measured in watts.
• What does t stand for? t stands for time. Time is measured in seconds.
• What does W stand for? W stands for work. Work is the amount of energy used to do something. It is measured in joules.
• What is the equation that relates power, time, and work? The equation that relates power, time, and work is:

P = W/t

where P is power, W is work, and t is time.

• What are the units of P, t, and W? The units of P are watts, the units of t are seconds, and the units of W are joules.
• What are the values of P and t in this problem? In this problem, P = 1200 watts and t = 54000 seconds.
• What is the value of W? We can find the value of W by substituting the values of P and t into the equation P = W/t:

W = Pt = (1200 watts)(54000 seconds) = 648 × 10^5 J = 6.48 × 10^7 J

• What are the units of W? The units of W are joules.
• What does 18 units mean? 18 units is the same as 18 kilowatt-hours (kWh). A kilowatt-hour is a unit of energy equal to the amount of energy used by a 1 kilowatt appliance in one hour.

In conclusion, the work done by the appliance is 6.48 × 10^7 joules, which is equivalent to 18 kilowatt-hours.

(c)If the energy of a ball falling from a height of 10 meters is reduced by 40%, how high will it rebound? (Ans: 6 m)

solution: The initial potential energy of the object is 100 J. When the object falls, its potential energy is converted into kinetic energy. When the object reaches the ground, its kinetic energy is zero. The remaining potential energy is the rebound energy.

The rebound energy is 60 J. Let the final height of the object be h2. The rebound potential energy is given by:

P.E.2 = mgh2

where m is the mass of the object, g is the acceleration due to gravity, and h2 is the final height of the object.

We know that P.E.2 = 60 J. Plugging this value into the equation, we get:

60 = mgh2

Dividing both sides of the equation by mg, we get:

h2 = 60/mg

We are given that the initial height of the object is 10 m. This is the same as the initial potential energy, since P.E.1 = mgh1. Plugging this value into the equation, we get:

h2 = 60/(10 * 9.81)

≈ 6 m

Therefore, the final height of the object is 6 meters.

(d)The velocity of a car increases from 54 km/hr to 72 km/hr. How much is the work done if the mass of the car is 1500 kg? (Ans.:131250J)

Answer: The work done to increase the velocity of a car is equal to the change in the car’s kinetic energy. The kinetic energy of a car is equal to its mass times its velocity squared.

In this case, the mass of the car is 1500 kg. The initial velocity of the car is 54 km/h. The final velocity of the car is 72 km/h.

To calculate the work done, we first need to convert the velocities into meters per second.

54 km/h = 54000 m / 3600 s = 15 m/s72 km/h = 72000 m / 3600 s = 20 m/s

The change in the car’s kinetic energy is:

(1500 kg x (20 m/s) ^²) – (1500 kg x (15 m/s)^²) = 131250 J

Therefore, the work done to increase the velocity of the car is 131250 J.

In other words, 131250 joules of energy were needed to increase the car’s velocity from 54 km/h to 72 km/h. This energy could have come from the car’s engine, or the force of gravity if the car was going uphill.

(e)Ravi applied a force of 10 N and moved a book 30 cm in the direction of the force. How much was the work done by Ravi? (Ans: 3 J)

Work is done when a force moves an object. The amount of work done is equal to the force applied times the distance moved.

In this case, Ravi applied a force of 10 N and moved the book 30 cm. So, the work done by Ravi is:

Work = Force x Distance= 10 N x 0.3 m= 3 J

In other words, Ravi did 3 joules of work by moving the book 30 centimeters in the direction of the force.