1. What is Energy?
The SI unit of energy is the Joule (J), just like work.
2. Different Forms of Energy
Energy exists in various forms, and it can change from one form to another. The main forms are:
Mechanical Energy: The energy possessed by an object due to its motion or position. It is of two types:
Kinetic Energy: The energy of a moving object (e.g., a rolling ball).
Potential Energy: The stored energy due to position or state (e.g., a stretched rubber band, water in a dam).
Heat Energy: The energy that causes a change in temperature.
Light Energy: The energy that allows us to see (e.g., from the sun or a lamp).
Chemical Energy: Energy stored in chemicals and released in reactions (e.g., in food, batteries).
Sound Energy: Energy produced by vibrating objects.
3. Sources of Energy
Where we get our energy from:
Renewable Sources: These can be replenished naturally (e.g., Solar, Wind, Water, Geothermal).
Non-Renewable Sources: These are limited and will run out one day (e.g., Coal, Petroleum, Natural Gas).
4. Law of Conservation of Energy
This is a very important law. It states that energy can neither be created nor destroyed; it can only be transformed from one form to another. The total amount of energy in the universe always remains constant. For example, when a ball falls, its potential energy decreases as its kinetic energy increases.
5. Energy and Our Future
The chapter often concludes by emphasizing the need to use energy wisely. Since non-renewable sources are getting depleted, we should focus on conserving energy and using more renewable sources for a sustainable future.
Test your self
A.Objective Questions
1. Write true or false for each statement
(a) A coolie does no work against the force of gravity while carrying a luggage on a road.
Ans: True.
(b) The energy stored in water of a dam is the kinetic energy.
Ans: False.
The energy stored in water of a dam is the potential energy.
(c) The energy of a flying kite is kinetic energy.
Ans: True.
(d) Work done by a boy depends on the time in which he does work.
Ans: False.
(e) Power spent by a body depends on the time for which it does work.
Ans: True.
2. Fill in the blanks
(a) Work is said to be done by a forte only when the body moves.
(b) Work done = Force × distance moved in direction of force.
(c) The energy of a body is its capacity to do work.
(d) The S.I. unit of energy is joule.
(e) The potential energy of a body is due to its state of rest or position and kinetic energy of body is due to its state of motion.
(f) Gravitational potential energy U = mass × force of gravity on unit mass × height.
(g) Kinetic energy = 1/2 × mass × (speed)2
(h) Power P=work done/time taken.
(i) The S . i. unit of power is watt
(j) I H.P. = 746 W
Ans:
(a) Work is said to be done by a forte only when the body moves.
(b) Work done = Force × distance moved in direction of force.
(c) The energy of a body is its capacity to do work.
(d) The S.I. unit of energy is joule.
(e) The potential energy of a body is due to its state of rest or position and kinetic energy of body is due to its state of motion.
(f) Gravitational potential energy U = mass × force of gravity on unit mass × height.
(g) Kinetic energy = 1/2 × mass × (speed)2
(h) Power P=work done/time taken.
(i) The S . i. unit of power is watt
(j) I H.P. = 746 W
3. Match the following
4. Select the correct alternative
(a) The S.I. unit of work is
- second
- metre
- joule
- newton
Ans: joule
(b) No work is done by a force if the body
- moves in direction of force
- does not move
- moves in opposite direction
- none of the these
Ans: does not move
(c) Two coolies A and B do some work in time 1 minute and 2 minute respectively. The power spent is
- same by both coolies
- is more by coolie A than by B
- is less by coolie A than by B
- nothing can be said.
Ans: is more by coolie A than by B
(d) The expression of power P is
- P = mgh
- P = P = 1/2 Mv2
- P = F × d
- P = F × d/t
Ans: P = F × d/t
(e) I H.P. ¡s equal to
- 1 W
- 1 J
- 746 J
- 746 W
Ans: 746 W
(f) When a boy doubles his speed, his kinetic energy becomes
- half
- double
- four times
- no change
Ans: four times
(g) A boy lifts a luggage from height 2 m to 4 m. The potential energy will become
- half
- double
- one-third
- one-fourth
Ans: Double
B. Short/Long Answer Questions
Question 1. Define work.
Ans: In physics, “work” has a very specific meaning. You only do work on an object when two things happen at the same time:
You apply a force to it.
If you push against a solid wall and it doesn’t budge, you haven’t done any scientific work on the wall, no matter how tired you feel.
The formula for work is: Work = Force × Displacement × cos θ (where θ is the angle between the force and movement).
A key example is carrying a heavy bag horizontally. Your upward force fights gravity, but the bag’s movement is forward. Since the force and motion are perpendicular, you are doing zero physics work on the bag.
The unit of work is the joule, which is a Newton-meter.
Question 2. When does a force perform work ?
Ans: In physics, “work” isn’t just about effort; it requires two specific things to happen at once:
The object must move in the direction of that force.
If either condition is missing, no scientific “work” is done.
Examples:
Positive Work: Lifting a box upwards. Your upward force and the box’s upward motion are in the same direction.
Zero Work: Pushing a wall that doesn’t budge (force, but no movement) or walking while carrying a suitcase (your upward force and the forward motion are perpendicular).
Negative Work: Slowing down a rolling ball by applying friction. The force of friction acts opposite to the direction of motion, draining the ball’s energy.
Question 3. State two conditions when no work is done by a force.
Ans: Two conditions when no work is done by a force are:
Zero Displacement: When the point of application of the force does not move. (Example: Pushing hard against a stationary wall.)
Force Perpendicular to Displacement: When the force acts at a right angle (90°) to the direction of the object’s displacement. (Example: Carrying a suitcase horizontally while walking.)
Question 4. In which of the following cases is work being done : (a) A boy pushing a rock (b) A boy climbing up the stairs (c) A coolie standing with a box in his head (d) A girl moving on the road.
Ans: (a) A boy pushing a rock
Yes, work is done because a force is applied and the rock moves.
(b) A boy climbing up the stairs
Yes, work is done against gravity as the boy moves upward.
(c) A coolie standing with a box in his head
No work is done because there is no movement of the box.
(d) A girl moving on the road
Yes, work is done because a force is applied to move her body forward.
Question 5. A coolie is moving on a road with a luggage on his head. Does he perform work against the force of gravity ? Give reason for your answer.
Ans: No, the coolie does not perform work against gravity.
Reason:
Work is done against gravity only when there is vertical displacement. Since the coolie is moving horizontally on the road, the force of gravity (which acts vertically downward) and his displacement (which is horizontal) are perpendicular to each other.
W=F⋅S⋅cosθ.
Here,
θ=90 ∘
, so
cos90 ∘ =0.
Hence, work done against gravity is zero.
Question 6. The moon is revolving around the earth in a circular path. How much work is done by the moon ?
Ans: The work done by the moon while revolving around the Earth is zero.
This is because the gravitational force of the Earth acts radially inward (towards the center), while the direction of the moon’s motion is tangential (perpendicular to the radius). Since the angle between the force and the direction of displacement is 90 degrees, and Work = Force × Displacement × cos(90°) = Force × Displacement × 0, the work done is zero.
Question 7. Write the expression for work done by a force,
Ans: In physics, work is defined as a measure of energy transfer that occurs when an object is moved by an external force. The amount of work done depends on two main factors: the magnitude of the force applied and the distance over which that force causes the object to move.
The most general expression for the work done (W) by a constant force is given by the dot product of the force vector (F) and the displacement vector (s). This can be written as: W = F • s
However, since force and displacement are vectors, the dot product accounts for the direction in which the force is applied. It considers the component of the force that acts along the direction of displacement.
A more practical and common form of this expression is:
W = F s cosθ
Let’s break down what each term in this expression represents:
W: This is the work done. Its SI unit is the joule (J), where 1 joule is equal to 1 newton-meter (N·m).
F: This is the magnitude of the constant force applied, measured in newtons (N).
s: This is the magnitude of the displacement of the object, measured in meters (m). Displacement is the straight-line distance between the starting and ending points, not the total path length traveled.
cosθ: This is the cosine of the angle (θ) between the direction of the applied force vector and the direction of the displacement vector.
The Importance of the Angle (θ)
The cosθ term is crucial because it tells us how effective the force is at causing displacement.
When θ = 0° (Force and Displacement are in the same direction):
cos0° = 1
Therefore, W = F s. This is the maximum positive work done. The force is most effective in transferring energy to the object.
When 0° < θ < 90°:
cosθ is positive but less than 1.
The work done is positive. Only a component of the force is acting in the direction of motion.
When θ = 90° (Force is Perpendicular to Displacement):
cos90° = 0
Therefore, W = 0. No work is done. A common example is when you carry a heavy bag horizontally. The upward force you apply is perpendicular to the horizontal displacement, so you are not doing work on the bag in the physics sense, despite feeling tired.
When 90° < θ ≤ 180°:
cosθ is negative.
The work done is negative. This happens when a force opposes the motion, like kinetic friction. In this case, the force is taking energy away from the object.
Question 8. State the S.I. unit of work and define it.
Ans: The joule is the unit for measuring work.
One joule of work is done when a one-newton force successfully moves an object a distance of one metre in the force’s direction.
Question 9. State two factors on which the work done on a body depends.
Ans: The amount of work done on an object depends on two things:
The Force Applied: A larger force does more work. Pushing a car is more work than pushing a bicycle.
The Distance Moved: The object must move in the force’s direction. Moving a box across a long room is more work than moving it a short distance.
If the object does not move, like when pushing a wall, then no work is done regardless of how hard you push.
Question 10. Define the term energy.
Ans: It is what allows objects to cause changes, such as moving, heating, or lighting something. Energy exists in various forms like heat, light, and motion, and it can be transferred from one object to another, but it cannot be created or destroyed.
Question 11. State the S.I. unit of energy.
Ans: The SI unit of energy is the joule (J).
Question 12. Define 1 joule of energy.
Ans: One joule is defined as the amount of energy transferred or the work done when a force of one newton is applied to an object, and it moves that object through a distance of one metre in the exact direction of the applied force.In simpler, more relatable terms, imagine gently pushing a small apple with one newton of force (which is about the weight of that apple) across a table. The energy you spend to move that apple exactly one metre is roughly equal to one joule.It is the standard unit of energy and work in the International System of Units (SI), named after the English physicist James Prescott Joule for his foundational work in the field of thermodynamics.
Question 13. How is work related to energy ?
Ans: Work transfers energy between objects or systems.
When you do work on an object, like lifting a book, you give it energy, increasing its own energy.
When an object does work, like a falling book pushing air aside, it spends its energy, transferring it away.
In this way, work is the bridge that allows energy to move and change form. This direct link is why both work and energy are measured in the same unit, the Joule (J).
Question 14. What are the two kinds of mechanical energy ?
Ans: 1. Kinetic Energy: Energy of Motion
Kinetic energy is the energy an object has because it is moving. The amount it has depends on its:
Mass: A heavier object moving at the same speed as a lighter one has more kinetic energy.
Velocity: Speed has a greater effect. Doubling an object’s speed quadruples its kinetic energy.
Examples: A rolling ball, a person running, a flowing river.
2. Potential Energy: Stored Energy
Potential energy is energy that is stored and waiting to be used, based on an object’s position or state.
Gravitational Potential Energy: This comes from an object’s height. The higher and heavier an object is, the more energy it stores.
Elastic Potential Energy: This is energy stored in stretched or compressed objects, like a drawn bow or a coiled spring.
Examples: A book on a high shelf, a roller coaster at the top of a hill, a stretched rubber band.
Question 15. What is potential energy ? State its unit.
Ans: Potential Energy is the energy stored in an object due to its position, shape, or state.
Examples:
A book on a high shelf has gravitational potential energy.
A stretched spring has elastic potential energy.
Its SI unit is the Joule (J).
Question 16. Give one example of a body that has potential energy, in each of the following : (a) due to its position at a height, (b) due to its elongated stretched state.
Ans: (a) Due to its position at a height:
A book placed on a high shelf has potential energy. Because of its elevated position relative to the floor, it stores energy. If the book is knocked off the shelf, this stored energy is converted into kinetic energy (the energy of motion) as it falls down.
(b) Due to its elongated stretched state:
A stretched rubber band has potential energy. When you stretch it, you are doing work against the elastic forces of the rubber band. This work is stored as potential energy. The moment you release one end, this stored energy is released, causing the rubber band to snap back to its original shape.
Question 17. State two factors on which the potential energy of a body at a certain height above the ground depends.
Ans: The potential energy of a body at a height depends on two factors:
Height: Potential energy is directly proportional to the height from the ground. Doubling the height results in double the potential energy. For example, a book on a higher shelf has more potential energy than the same book on a lower shelf.
Mass: Potential energy is also directly proportional to the mass of the object. A heavier object at the same height will possess more potential energy than a lighter one. For instance, a large rock lifted up has more potential energy than a small stone at the same height.
Question 18. Two bodies A and B of masses 10 kg and 20 kg respectively are at the same height above the ground. Which of the two has greater potential energy ?
Ans: Body B (20 kg mass) has greater potential energy.
Explanation:
Potential energy is calculated as
PE=mgh.
Since both bodies are at the same height and g is constant,
the potential energy depends only on mass.
Here, mass of B (20 kg) is greater than mass of A (10 kg),
so B has greater potential energy.
Question 19. A bucket full of water is on the first floor of your house and another identical bucket with same quantity of water is kept on the second floor. Which of the two has greater potential energy ?
Ans: This is because potential energy increases with height. Since the second floor is higher than the first floor, the bucket of water placed there has more stored energy due to its elevated position.
Question 20. Write the expression for the gravitational potential energy explaining the meaning of the symbols used. Answer:
Ans: The gravitational potential energy
U for two masses
M and m separated by distance
r is given by:
U=−GMm/r
Symbols:
G: Universal gravitational constant ()
M: Mass of the larger body (e.g., Earth)
m: Mass of the smaller object
r: Distance between the centers of M and m
Negative Sign Meaning:
The potential energy is zero when r→∞.
At finite distances,U is negative, meaning the system is bound. Energy must be supplied to separate the masses completely.
Near Earth’s Surface:
For small height changes
h (where h≪R E , Earth’s radius), the formula simplifies to:
U=mgh
Here,
g≈9.8m/s 2 , and h is measured from a chosen reference level (like the ground).
Question 21. A body of mass m is moved from ground to a height h. If force of gravity on mass of 1 kg is g newton, find : (a) the force needed to lift the body, (b) the work done in lifting the body and (c) the potential energy stored in the body.
Ans: (a) Force needed to lift the body
The force of gravity on mass m is mg.
To lift the body at a constant speed (without acceleration), the force needed is equal to the weight of the body:
F=m×g newton
(b) Work done in lifting the body
Work done = Force × Displacement (in the direction of force)
W=F×h=mgh joule
(c) Potential energy stored in the body
The work done against gravity is stored as gravitational potential energy:
Potential Energy=mgh joule
Question 22. Define the term kinetic energy. Give one example of a body which possesses kinetic energy.
Ans: Kinetic Energy
Kinetic energy is the energy possessed by a body due to its motion. Any object that is moving has kinetic energy. The amount of this energy depends on two factors: the mass of the object and its velocity. The greater the mass of the object and the faster it is moving, the more kinetic energy it possesses.
Example of a Body Possessing Kinetic Energy
A clear example of a body possessing kinetic energy is a cricket ball rolling on the ground. As the ball moves across the field, it has mass and velocity, and therefore it possesses kinetic energy. This energy is evident because if the rolling ball hits the stumps, it can displace the bails, doing work by virtue of its motion.
Question 23. State two factors on which the kinetic energy of a moving body depends.
Ans: The kinetic energy of a moving object depends on its mass and velocity.
Mass: The heavier the object, the more kinetic energy it has. A truck has more energy than a bicycle at the same speed.
Velocity: Speed has a much greater effect. Doubling the speed quadruples the kinetic energy, which is why high-speed crashes are so much more destructive.
Question 24. Two toy-cars A and Bof masses 200 g and 500 g respectively are moving with the same speed. Which of the two has greater kinetic energy ?
Ans: Car B has greater kinetic energy.
Explanation:
Kinetic energy is given by
KE=1/2mv2
Since both cars have the same speed, kinetic energy depends on mass.
Car B has a larger mass (500 g) than Car A (200 g), so Car B will have more kinetic energy.
Question 25. A cyclist doubled his speed. How will his kinetic energy change: increase, decrease or remain the same ?
Ans: When the cyclist doubles his speed, the kinetic energy increases to four times the original value. This happens because kinetic energy is proportional to the square of the speed.
Question 26. Write the expression for the kinetic energy of a body explaining the meaning of the symbols used.
Ans: Kinetic energy (K), measured in Joules, is the energy an object has from its motion. It’s calculated as:
K = ½mv²
m is the object’s mass in kilograms (kg).
v is its velocity in meters per second (m/s).
The formula works this way because of how objects are accelerated from rest. The key feature is that velocity is squared (v²). This means speed has a massive impact.
For example, doubling an object’s speed quadruples its kinetic energy. This is why a high-speed car crash is far more destructive than a low-speed one.
Question 27. A ball of mass m is moving with a speed v. What is its kinetic energy ?
Ans: The kinetic energy of a moving ball is calculated as ½ × m × v².
This means:
Kinetic energy is directly proportional to its mass. Doubling the mass doubles the kinetic energy.
Kinetic energy is proportional to the square of its speed. This has a much greater effect:
Doubling the speed makes the kinetic energy four times greater.
Tripling the speed makes it nine times greater.
Question 28. Name the form of energy stored in a wound up spring of a watch
Ans: The form of energy stored in a wound-up spring of a watch is Elastic Potential Energy.
Explanation
When you wind the spring of a watch, you are doing work against the spring’s natural state. This work is not lost; instead, it gets stored within the spring. The act of winding twists and tightens the spring, causing its coils to deform. Because the spring is made of a resilient metal, it resists this deformation and has a strong tendency to want to return to its original, relaxed shape.This stored energy, which is held ready until it is released, is known as Elastic Potential Energy. It is “potential” because it has the potential to do work in the future, and “elastic” because it is stored in an object that has been stretched or compressed.In a watch mechanism, this stored energy is then released in a very slow and controlled manner through the escapement mechanism. The gradual unwinding of the spring provides the steady force that turns the gears, which in turn move the hands of the watch, converting the stored elastic potential energy into the kinetic energy of the moving parts.
Question 29. Can a body possess energy even when it is not in motion ? Explain your answer with an example.
Ans: Yes, a body can possess energy even when it is not in motion.Energy possessed by a body due to its state or position is called potential energy. Since the body is not moving, it has no kinetic energy, but it stores energy that can be used to do work in the future.
Example:
A book placed on a table is not moving. However, if we push it off the edge, it falls down. This is because when the book was on the table, it possessed gravitational potential energy due to its height above the ground. This stored energy converted into kinetic energy (motion) as it fell.
Question 30. Name the type of energy (kinetic or potential) possessed by the following: (a) A moving cricket ball. (b) A stone at rest on the top of a building. (c) A compressed spring. (d) A moving bus. (e) A bullet fired from a gun. (f) Water flowing in a river. (g) A stretched rubber band.
Ans: (a) A moving cricket ball → Kinetic energy
(b) A stone at rest on the top of a building → Potential energy
(c) A compressed spring → Potential energy
(d) A moving bus → Kinetic energy
(e) A bullet fired from a gun → Kinetic energy
(f) Water flowing in a river → Kinetic energy
(g) A stretched rubber band → Potential energy
Question 31. Give an example to show the conversion of potential energy to kinetic energy when put in use.
Ans: A rock sitting at the top of a hill is a great example of energy conversion.While at the summit, the rock stores energy due to its height. This stored power is called potential energy.Once pushed, the rock begins to roll downhill.. This energy doesn’t disappear; it transforms into kinetic energy, which is the energy of motion. The rock picks up speed as this conversion happens.So, the journey downhill is simply the rock’s stored potential energy being changed into the kinetic energy of its movement. At the top, all the energy is potential; at the bottom, it has mostly become kinetic, making the rock move fast.
Question 32. State the energy changes that occur in a watch spring while it unwinds.
Ans: When we wind a watch, we do work by twisting the crown. This work is stored in the mainspring (the coiled spring inside) as potential energy. This potential energy is specifically elastic potential energy because it is due to the deformation (coiling) of the spring.As the watch spring slowly unwinds, this stored elastic potential energy is gradually converted into other forms of energy. The primary energy change is into kinetic energy, which is the energy of motion. This kinetic energy is transferred through a series of gears and components called the escapement, which regulates the release of energy to power the watch.
This kinetic energy is used for two main purposes:
To move the hands of the watch around the dial.
To drive the internal mechanisms that keep time.
Finally, due to friction between the moving parts (gears, pivots, etc.), some of the initial potential energy is inevitably converted into heat energy. This heat is dissipated into the surroundings and is not a useful form of energy for the watch’s operation.
Elastic Potential Energy → Kinetic Energy + Heat Energy
Question 33. Give reasons for the following: (a) No work is done ¡fa man ¡s pushing against a wall. (b) Hammer drives a nail into the wood only when it ¡s lifted up and then struck. (c) A horse and a dog are running with the same speed. Which one of them has more kinetic energy than the other. (d) A teacher moving around in the class is doing work but a child standing and reading a book is not doing any work
Ans: (a) No work is done when a man pushes against a wall because the wall does not move.Here, displacement is zero, so work is zero.
(b) A hammer drives a nail into wood only when it is lifted and then struck because:
Lifting the hammer gives it potential energy.When struck, this energy converts into kinetic energy, which is transferred to the nail, doing work against the wood’s resistance.
(c) A horse has more kinetic energy than a dog running at the same speed because:
Kinetic energy depends on mass and speed.A horse has much more mass than a dog, so its kinetic energy is greater.
(d) A teacher moving around in the class does work because:
Work involves force and displacement — the teacher applies muscular force to move.A child standing and reading applies no displacement in the force direction, so no work is done.
Question 34. State the energy changes in the following while ¡n use. (a) An electric bulb (b) An electric oven (c) A loud speaker (d) A microphone (e) An electric motor
Ans: (a) Electric Bulb
It changes electrical energy mainly into light energy. A lot of energy is also wasted as heat, which is why the bulb gets hot.
(b) Electric Oven
It converts electrical energy into heat energy. A heating element resists the electric current, becomes hot, and warms the oven.
(c) Loudspeaker
It transforms electrical energy from an audio source into sound energy. A vibrating diaphragm creates sound waves in the air.
(d) Microphone
It works opposite to a loudspeaker. Sound energy makes a diaphragm vibrate, producing a corresponding electrical signal.
(e) Electric Motor
It changes electrical energy into mechanical energy (rotation or motion), used to run machines like fans, mixers, or vehicles.
C. Numericals
Question 1. A force of 30 N acts on a body and moves it through a distance of 5 m in the direction of force. Calculate the work done by the force.
Ans: Step 1: Identify the known values
Force, F=30 N
Displacement, s=5 m
Direction: Force and displacement are in the same direction.
Step 2: Use the work formula
W=F×s
Step 3: Substitute values
W=30×5=150 J
Final Answer:150 J
Question 2. A man lifts a mass of 20 kg to a height of 2.5 m. Assuming that the force of gravity on 1 kg mass is 10 N, find the work done by the man.
Ans: Step 1: Find the force exerted by gravity on the mass
Mass = 20 kg
Gravity on 1 kg = 10 N
So, weight (force) = 20×10=200N
Step 2: Find the work done
Work = Force × Distance
Work = 200N×2.5m
Work = 500J
Final Answer:500
Question 3. A body when acted upon by a force of 10 kgf moves to a distance 0.5 m in the direction of force.Find the work done by the force. Take 1 kgf = 10 N.
Ans: Step 1: Convert force into Newtons
Given:
Force = 10 kgf
1 kgf = 10 N
So, Force = 10×10=100N
Step 2: Identify displacement
Displacement in the direction of force = 0.5 m
Step 3: Work done formula
Work=Force×Displacement
Work=100×0.5
Work=50J
Final Answer:50
Question 4. Two bodies of the same masses are placed at heights h and 2h. Compare their gravitational potential energy.
Ans: For two equal masses, gravitational potential energy is directly proportional to height.
The object at height h has GPE =mgh.
The object at height 2h has GPE =mg(2h)=2mgh.
So the ratio of their GPE is
2mgh/mgh=2
Thus, the ratio of GPE at 2h to GPE at 2:1.
Question 5. Find the gravitational potential energy of 2.5 kg mass kept at a height of 15 m above the ground. The force of gravity on mass 1 kg is 10 n.
Ans: Step 1: Identify known values
Mass m=2.5 kg
Height h=15 m
Gravity on 1 kg = 10 N, so
g=10 N/kg=10 m/s 2
Step 2: Formula for gravitational potential energy
PE=m×g×h
Step 3: Substitute values
PE=2.5×10×15
PE=25×15=375 J
Final Answer: 375 J
Question 6. The gravitational potential energy stored in a box of weight 150 kgf is 1.5 x 104 J. Find the height of the box. Take l kgf = 10 N.
Ans: Step 1: Convert weight to Newtons
Weight
W=150 kgf
Given
1 kgf=10 N,
W=150×10=1500 N
Step 2: Use gravitational potential energy formula
Potential Energy=W×h
1.5×10*4=1500×h
Step 3: Solve for height
h=1.5×10*4/1500=15000/1500=10 m
h=10 m
Final Answer:10
Question 7. The potential energy of a body of mass 0.5 kg increases by 100 J when it is taken to the top of a tower from ground. If force of gravity on 1 kg is 10 N, what is the height of the tower ?
Ans: Step 1: Understanding the Problem
We are told that a body with a mass of 0.5 kg gains 100 Joules of potential energy. We are also given a key piece of information: the force of gravity on a 1 kg mass is 10 Newtons. This is another way of saying that the acceleration due to gravity, g, is 10 m/s².Our goal is to find the height the body was raised to, which in this context is the height of the tower.
Step 2: Recalling the Physics Concept
The gravitational potential energy (PE) gained by an object is directly related to its mass, the strength of gravity, and the height it is raised. The formula that connects these quantities is:
Change in Potential Energy = mass × gravity × height
Or, in mathematical terms:
ΔPE = m × g × h
Step 3: Substituting the Given Values
We plug the known values from the problem into this formula:
ΔPE = 100 J
m = 0.5 kg
g = 10 N/kg (or m/s²)
So the equation becomes:
100 = 0.5 × 10 × h
Step 4: Solving for Height (h)
Now we perform the calculation step-by-step:
First, multiply 0.5 and 10:
100 = 5 × h
To solve for h, we divide both sides of the equation by 5:
h = 100 ÷ 5
This gives us the final answer:
h = 20 meters
Step 5: Final Conclusion
This is the vertical distance the 0.5 kg body was lifted to achieve a gain of 100 Joules of potential energy.
Question 8. A body of mass 60 kg is moving with a speed 50 m s_1. Find its kinetic energy.
Ans: Step 1: Understanding the Problem
We are tasked with finding the kinetic energy of a moving body. We are given:
The body’s mass (m) = 60 kg
The body’s speed (v) = 50 m/s
Step 2: The Formula for Kinetic Energy
The formula that connects mass and speed to kinetic energy is a fundamental one in physics:
Kinetic Energy (K.E.) = ½ × m × v²
Where:
m is the mass in kilograms (kg)
v is the speed in meters per second (m/s)
The resulting energy is in Joules (J)
Step 3: Substituting the Given Values
Now, we simply plug our known values into the formula.
K.E. = ½ × 60 kg × (50 m/s)²
Step 4: Performing the Calculation
Let’s break this down into smaller parts to make it clear.
First, calculate (50 m/s)².
50 × 50 = 2500 m²/s²
Now, calculate ½ × 60 kg.
This is the same as 60 ÷ 2 = 30 kg
Finally, multiply these two results together:
30 kg × 2500 m²/s² = 75,000 kg·m²/s²
In the standard unit of energy, Joules (J), 1 Joule is defined as 1 kg·m²/s².
Step 5: Final Answer
Therefore, the kinetic energy of the body is: 75,000 Joules (J)
Question 9 A truck of mass 1000 kg, increases its speed from 36 km h-1 to 72 km h-1. Find the increase in its kinetic energy.
Ans: Step 1: Note down the given information
Mass of the truck,
m=1000 kg
Initial speed, v=36 km h −1
Final speed, v =72 km h −1
Step 2: Convert speeds from km/h to m/s
The formula for conversion is:
1km h−1=1000/3600 m/s=5/18 m/s
Initial speed, v1=36×5/18=10 m/s
Final speed, v2=72×5/18=20 m/s
Step 3: Write the formula for kinetic energy
m moving with speed
v is given by:
K.E.=1/2mv
Step 4: Calculate the initial and final kinetic energies
Initial Kinetic Energy,
K1=1/2×1000×(10)2
K1=500×100=50000 J
Final Kinetic Energy,
K2=1/2×1000×(20)2
k2 =500×400=200000 J
Step 5: Find the increase in kinetic energy
The increase is the difference between the final and initial kinetic energies.
ΔK=K 2−K 1
=200000−50000=150000 J
Final Answer:150000J
The increase in the kinetic energy of the truck is 150,000 Joules.
Question 10. A car is moving with a speed of 15 km h-1 and another identical car is moving with a speed of 30 km h-1. Compare their kinetic energy.
Ans: When two identical cars are compared, one moving at 15 km/h and the other at 30 km/h, the faster car has twice the speed.
Kinetic energy depends on the square of the speed:
KE = ½ × mass × (speed)²
So, doubling the speed increases the kinetic energy by 2² = 4 times.
Therefore, the car moving at 30 km/h has four times more kinetic energy than the car moving at 15 km/h.
Question 11. A pump raises water by spending 4 × 105 J of energy in 10 s. Find the power of pump.
Ans: Step 1: Understanding the Problem
We are given two pieces of information:
The total energy spent is 400,000 Joules (which is written as 4×10*5 J).
This energy was used over a time of 10 seconds.
Our goal is to find the power. In physics, power is defined as the rate at which energy is used or transferred. It tells us how fast the work is being done.
Step 2: The Formula for Power
The relationship between power (P), energy (E), and time (t) is given by a straightforward formula:
P=Et
Where:P is Power in Watts (W)
E is Energy in Joules (J)
t is Time in seconds (s)
Step 3: Substituting the Given Values
Now, we simply plug our known values into the formula.
P=4×10*5 J
P= 10 s
Step 4: Performing the Calculation
Dividing 4×10 *5 by 10 is simple.The number 4×10 *5 means 4 followed by 5 zeros, which is 400,000.
Dividing 400,000 by 10 gives us 40,000.
We can also think of it in terms of exponents:
4×10*5/10=4×10*5/10*1=4×10(5−1)=4×10*4
And 4×10 *4 is equal to 40,000.
So,
P=40,000 W
Question 12. It takes 20 s for a girl A to climb up the stairs while girl B takes 15 s for the same job. Compare : (i) the work done and (ii) the power spent by then.
Ans: (i) Work done:
Both girls climb the same stairs, so vertical height and hence work done against gravity is the same.
Ratio of work done = 1 : 1
(ii) Power spent:
Power = Work / Time
Since work is the same, power is inversely proportional to time.
Time ratio (A : B) = 20 : 15 = 4 : 3
So, power ratio (A : B) = 3 : 4
