NCERT Class 9 Science Solutions: Work and Energy
Question:
Look at the activity below. Reason out whether or not work is done in the light of your understanding of the term ‘work’.
A wind-mill is lifting water from a well.
Concept in a Minute:
Work is done when a force causes a displacement in the direction of the force. Mathematically, Work (W) = Force (F) × Displacement (d) × cos(θ), where θ is the angle between the force and displacement. If there is no displacement, or if the displacement is perpendicular to the force, then no work is done.
Explanation:
In the given activity, a windmill is lifting water from a well.
1. Force: The windmill exerts an upward force to lift the water. This force is necessary to overcome gravity acting on the water.
2. Displacement: The water is being moved upwards from the well to a higher level. This constitutes a displacement in the upward direction.
3. Direction of Force and Displacement: The force applied by the windmill is in the upward direction, and the displacement of the water is also in the upward direction. Therefore, the force and displacement are in the same direction (or at least have a component in the same direction).
Since there is a force applied, and this force causes a displacement of the water in the direction of the force, work is being done by the windmill on the water. The windmill is transferring energy to the water to lift it.
Detailed Steps:
1. Identify the object on which work is being done: The water being lifted from the well.
2. Identify the force acting on the object: The force exerted by the windmill that causes the water to move upwards.
3. Determine if there is displacement: Yes, the water is displaced upwards.
4. Check if the force causes the displacement: Yes, the upward force from the windmill is causing the upward displacement.
5. Conclude whether work is done based on the definition of work: Since a force is applied and it results in a displacement in the direction of the force, work is done.
Answer: Yes, work is done.
Question:
Calculate the work required to be done to stop a car of 1500 kg moving at a velocity of 60 km/h?
Concept in a Minute:
The work required to stop a moving object is equal to the change in its kinetic energy. Kinetic energy is the energy of motion and is calculated using the formula KE = 1/2 * m * v^2, where m is the mass and v is the velocity. Work-energy theorem states that the work done on an object is equal to its change in kinetic energy. To stop an object, the final kinetic energy is zero, so the work done is equal to the initial kinetic energy with a negative sign (representing energy being removed).
Explanation:
1. Identify the given quantities:
– Mass of the car (m) = 1500 kg
– Initial velocity of the car (v) = 60 km/h
2. Convert the velocity from km/h to m/s, as SI units are required for calculations:
– v = 60 km/h
– To convert km/h to m/s, multiply by (1000 m / 1 km) * (1 h / 3600 s) = 5/18
– v = 60 * (5/18) m/s = (300/18) m/s = 50/3 m/s
3. Calculate the initial kinetic energy (KE_initial) of the car:
– KE_initial = 1/2 * m * v^2
– KE_initial = 1/2 * 1500 kg * (50/3 m/s)^2
– KE_initial = 1/2 * 1500 * (2500/9) J
– KE_initial = 750 * (2500/9) J
– KE_initial = (1875000/9) J
– KE_initial = 208333.33 J (approximately)
4. Determine the final kinetic energy (KE_final) of the car:
– Since the car is brought to rest, its final velocity is 0 m/s.
– KE_final = 1/2 * m * (0 m/s)^2 = 0 J
5. Calculate the work done (W) using the work-energy theorem:
– Work done (W) = Change in Kinetic Energy = KE_final – KE_initial
– W = 0 J – 208333.33 J
– W = -208333.33 J
6. The work required to stop the car is the magnitude of this work, implying the energy that needs to be dissipated. Therefore, the work required is 208333.33 J (approximately).
Final Answer: The work required to be done to stop the car is approximately 208333.33 Joules.
Question:
What is the work done by the force of gravity on a satellite moving round the earth? Justify your answer.
Concept in a Minute:
Work done is defined as the product of force and displacement in the direction of the force. For circular motion, the force is always perpendicular to the direction of displacement.
Explanation:
The force of gravity acting on a satellite moving around the Earth is a centripetal force. This force is always directed towards the center of the Earth.
The motion of the satellite is circular (or elliptical, but for simplicity, let’s consider circular). In circular motion, the velocity of the satellite is always tangential to the circular path at any given point. The displacement of the satellite over an infinitesimally small time interval is along its velocity, i.e., tangential to the path.
The force of gravity (F) is directed radially inwards (towards the Earth’s center), while the instantaneous displacement (ds) of the satellite is tangential to its orbit.
The angle between the force of gravity and the displacement of the satellite is always 90 degrees.
The work done (W) by a force is given by the formula:
W = F * ds * cos(theta)
where F is the magnitude of the force, ds is the magnitude of the displacement, and theta is the angle between the force and the displacement.
In this case, theta = 90 degrees.
Since cos(90 degrees) = 0, the work done by the force of gravity on the satellite is:
W = F * ds * cos(90) = F * ds * 0 = 0 Joules.
Therefore, the work done by the force of gravity on a satellite moving around the Earth is zero. This is because the force of gravity is always perpendicular to the direction of the satellite’s instantaneous velocity and displacement, and thus it does not contribute to changing the satellite’s kinetic energy. The gravitational force only changes the direction of the satellite’s motion, not its speed.
Question:
Can there be displacement of an object in the absence of any force acting on it? Think. Discuss this question with your friends and teacher.
Concept in a Minute:
Newton’s First Law of Motion (Law of Inertia). This law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.
Explanation:
Yes, there can be displacement of an object in the absence of any force acting on it, but only under specific conditions described by Newton’s First Law of Motion.
If an object is already in motion and there are no external forces (like friction, air resistance, or gravity acting to change its speed or direction) acting on it, it will continue to move with a constant velocity (meaning it will maintain its speed and direction) indefinitely. Therefore, it will undergo displacement over time.
For example, imagine an astronaut in outer space, far away from any celestial bodies. If they give a tool a gentle push, and there’s no air resistance or other forces, the tool will continue to travel in a straight line at a constant speed forever, undergoing displacement even though no force is continuously acting on it. The initial push was the force that set it in motion, but once in motion, it continues without further applied force.
However, if the object is initially at rest, it will remain at rest in the absence of a force. To achieve displacement from rest, a force is always required. The question implies displacement can occur *in the absence of any force acting on it*, which points to the scenario of an object *already in motion* and then experiencing no net force.
Question:
An electric heater is rated 1500 W. How much energy does it use in 10 hours?
Concept in a Minute:
The key concept is the relationship between power, energy, and time. Power is the rate at which energy is transferred or used. The formula connecting these is: Energy = Power × Time.
Explanation:
The electric heater is rated at a power of 1500 Watts (W). This means it consumes 1500 Joules of energy every second.
The time for which the heater is used is given as 10 hours.
To find the total energy used, we need to multiply the power by the time. However, the units must be consistent. Power is in Watts (Joules per second), so time should be in seconds.
First, convert the time from hours to seconds:
1 hour = 60 minutes
1 minute = 60 seconds
So, 1 hour = 60 × 60 = 3600 seconds.
Therefore, 10 hours = 10 × 3600 seconds = 36000 seconds.
Now, calculate the energy used:
Energy = Power × Time
Energy = 1500 W × 36000 s
Energy = 54,000,000 Joules (J)
The energy can also be expressed in kilowatt-hours (kWh), which is a common unit for electrical energy consumption.
To convert Watts to kilowatts, divide by 1000:
Power = 1500 W / 1000 = 1.5 kW
Convert time from hours to hours (it’s already in hours):
Time = 10 hours
Now, calculate energy in kWh:
Energy = Power (in kW) × Time (in hours)
Energy = 1.5 kW × 10 hours
Energy = 15 kWh
So, the electric heater uses 54,000,000 Joules or 15 kilowatt-hours of energy in 10 hours.
Question:
Soni says that the acceleration in an object could be zero even when several forces are acting on it. Do you agree with her? Why?
Concept in a Minute:
Newton’s Second Law of Motion states that the net force acting on an object is equal to the product of its mass and acceleration (F_net = ma). Acceleration is the rate of change of velocity. If the net force is zero, then the acceleration must also be zero.
Explanation:
Yes, I agree with Soni. According to Newton’s Second Law of Motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, this is expressed as:
F_net = ma
where:
F_net is the net force acting on the object
m is the mass of the object
a is the acceleration of the object
If the acceleration (a) of the object is zero, then from the equation above, the net force (F_net) acting on the object must also be zero. This can happen even when several forces are acting on the object, provided that these forces are balanced. When forces are balanced, they cancel each other out, resulting in a net force of zero. For example, if an object is at rest or moving with a constant velocity, its acceleration is zero, and the vector sum of all forces acting on it is zero. A common example is an object placed on a table; gravity pulls it down, but the normal force from the table pushes it up with an equal and opposite force, resulting in zero net force and zero acceleration.
Question:
When do we say that work is done?
Concept in a Minute:
Work is a physics concept that describes the transfer of energy when a force causes an object to move a certain distance. For work to be done, two conditions must be met: there must be a force applied, and the object must move in the direction of the applied force.
Explanation:
Work is done when a force causes displacement of an object. Specifically, work (W) is defined as the product of the applied force (F) and the displacement (d) of the object in the direction of the force. Mathematically, this is expressed as:
W = F × d
Therefore, we say that work is done in the following situations:
1. A force is applied to an object.
2. The object moves (displaces) as a result of the applied force.
3. The displacement of the object has a component in the direction of the applied force.
If an object is pushed but does not move, no work is done, even though a force is being applied. Similarly, if an object moves on its own without any external force acting on it, no work is done by an external agent. If the force is applied perpendicular to the direction of motion, no work is done by that force (e.g., a person carrying a load on a horizontal surface walks forward; the force of gravity on the load is downwards, and the motion is horizontal, so no work is done by gravity in the direction of motion).
Question:
The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of energy? Why?
Concept in a Minute:
Law of Conservation of Energy states that energy cannot be created or destroyed, only transformed from one form to another. For a freely falling object, the relevant energy forms are potential energy (energy due to height) and kinetic energy (energy due to motion).
Explanation:
No, the progressive decrease in the potential energy of a freely falling object does not violate the law of conservation of energy. As the object falls, its height above the ground decreases. Potential energy is directly proportional to height (PE = mgh). Therefore, as height decreases, potential energy also decreases.
However, as the object falls, it gains speed. Kinetic energy is directly proportional to the square of velocity (KE = 1/2 mv^2). So, as the object’s speed increases, its kinetic energy increases.
The law of conservation of energy states that the total mechanical energy (the sum of potential energy and kinetic energy) of the object remains constant, assuming no external forces like air resistance are doing significant work. As potential energy decreases, kinetic energy increases by an exactly equal amount, ensuring that the total energy (PE + KE) stays the same throughout the fall. The potential energy is being transformed into kinetic energy.
Question:
Look at the activity below. Reason out whether or not work is done in the light of your understanding of the term ‘work’.
An engine is pulling a train.
Concept in a Minute:
Work is done when a force causes displacement in the direction of the force. Mathematically, Work (W) = Force (F) × Displacement (d) × cos(θ), where θ is the angle between the force and displacement. If there is no displacement or the displacement is perpendicular to the force, no work is done.
Explanation:
In this activity, an engine is pulling a train. For work to be done, two conditions must be met:
1. A force must be applied.
2. There must be a displacement in the direction of the applied force.
In the given scenario, the engine applies a force to pull the train. Since the train is being pulled, it is moving and therefore undergoing displacement. The force exerted by the engine is in the direction of the train’s movement (forward). As there is both a force applied by the engine and a displacement of the train in the direction of that force, work is being done.
The force exerted by the engine causes the train to move from one point to another, which is a displacement. Since the force and displacement are in the same direction, the angle θ between them is 0 degrees, and cos(0°) = 1. Therefore, the work done by the engine on the train is positive and non-zero.
Question:
An object thrown at a certain angle to the ground moves in a curved path and falls back to the ground. The initial and the final points of the path of the object lie on the same horizontal line. What is the work done by the force of gravity on the object?
Concept in a Minute:
Work done by a force is defined as the product of the force and the displacement of the object in the direction of the force. Mathematically, Work Done (W) = Force (F) × Displacement (d) × cos(θ), where θ is the angle between the force and displacement. For gravity, the force is always downwards.
Explanation:
The force of gravity acts vertically downwards on the object throughout its motion. The object is thrown at a certain angle to the ground and follows a curved path, eventually falling back to the ground. The problem states that the initial and final points of the path lie on the same horizontal line. This means that the net vertical displacement of the object is zero. Since work done by gravity depends on the vertical component of displacement, and the net vertical displacement is zero, the work done by the force of gravity on the object is zero. Even though the object moves horizontally and has vertical displacement during its trajectory, the upward vertical displacement is exactly cancelled out by the downward vertical displacement when it returns to the same horizontal level. Therefore, the total work done by gravity over the entire path is zero.
Question:
Look at the activity below. Reason out whether or not work is done in the light of your understanding of the term ‘work’.
A green plant is carrying out photosynthesis.
Concept in a Minute:
Work is done when a force causes displacement. In physics, work is defined as the product of force and displacement in the direction of the force. Mathematically, Work (W) = Force (F) × Displacement (d) × cos(θ), where θ is the angle between the force and displacement. For work to be done, both a force and a displacement in the direction of the force must be present.
Explanation:
In the given activity, a green plant is carrying out photosynthesis. Photosynthesis is a biological process where plants use sunlight, water, and carbon dioxide to create their own food (glucose) and release oxygen. While this process involves chemical reactions and energy transformations, it does not involve any physical force being applied by the plant that causes a displacement of an external object. The plant itself might grow or change shape over time due to metabolic processes, but this internal change is not considered “work” in the physics sense as it doesn’t involve the plant exerting a force on an external body to move it. Therefore, in the context of physics, no work is done by the green plant carrying out photosynthesis.
Question:
A certain household has consumed 250 units of energy during a month. How much energy is this in joules?
Concept in a Minute:
The question requires converting units of electrical energy from kilowatt-hours (kWh) to joules (J). The fundamental relationship is that 1 kWh is equal to 3.6 million joules.
Explanation:
The unit “units of energy” commonly used in households refers to kilowatt-hours (kWh).
We are given that the household consumed 250 units of energy.
This means the consumption is 250 kWh.
To convert kilowatt-hours to joules, we use the conversion factor:
1 kWh = 1 kilowatt × 1 hour
1 kilowatt = 1000 watts (W)
1 hour = 3600 seconds (s)
So, 1 kWh = 1000 W × 3600 s
Since power (Watt) is energy per unit time (Joule per second), we have:
1 W = 1 J/s
Therefore, 1 kWh = 1000 J/s × 3600 s
1 kWh = 3,600,000 joules (J)
Now, we can convert the given consumption from kWh to joules:
Energy in joules = Energy in kWh × (3.6 × 10^6 J/kWh)
Energy in joules = 250 kWh × 3.6 × 10^6 J/kWh
Energy in joules = 250 × 3.6 × 10^6 J
Energy in joules = 900 × 10^6 J
Energy in joules = 9 × 10^8 J
Therefore, 250 units of energy consumed by the household is equal to 9 × 10^8 joules.
Question:
A freely falling object eventually stops on reaching the ground. What happens to its kinetic energy?
Concept in a Minute:
Conservation of Energy, Kinetic Energy, Potential Energy. When an object falls, its potential energy is converted into kinetic energy. Upon impact, this energy is transformed into other forms.
Explanation:
A freely falling object possesses gravitational potential energy due to its height above the ground. As it falls, this potential energy is converted into kinetic energy, which is the energy of motion. When the object strikes the ground, its motion ceases, meaning its kinetic energy becomes zero. However, the kinetic energy is not destroyed. It is transformed into other forms of energy, primarily:
1. Heat energy: Due to friction with the air and the impact with the ground.
2. Sound energy: The audible “thud” or “bang” produced upon impact.
3. Energy to deform the object and the ground: Some energy is used to cause slight deformation of the object and the surface it hits.
Therefore, while the kinetic energy of the object itself becomes zero upon stopping, it is converted into other forms of energy.
Question:
Does the transfer of energy take place when you push a huge rock with all your might and fail to move it? Where is the energy you spend going?
Concept in a Minute:
Work done is defined as the product of force applied and the distance moved in the direction of the force. Mathematically, Work (W) = Force (F) × Distance (d). Energy transfer occurs when work is done. If there is no displacement, then no work is done. Energy spent is converted into other forms, often heat due to internal friction.
Explanation:
No, the transfer of energy, in the sense of doing work on the rock, does not take place when you push a huge rock with all your might and fail to move it.
According to the definition of work in physics, work is done only when a force causes a displacement. Since the rock does not move (displacement is zero), no work is done on the rock.
The energy you spend is not transferred to the rock as mechanical work. Instead, the energy is converted into heat within your body due to metabolic processes and muscular effort. This heat is then dissipated into the surroundings. You will feel tired because your muscles are using energy and generating heat.
Question:
An object of mass, m is moving with a constant velocity, v. How much work should be done on the object in order to bring the object to rest?
Concept in a Minute:
Work-Energy Theorem. This theorem states that the work done on an object is equal to the change in its kinetic energy. Kinetic energy is the energy an object possesses due to its motion and is calculated as KE = 0.5 * m * v^2, where m is the mass and v is the velocity.
Explanation:
The object is initially moving with a constant velocity v, so it possesses kinetic energy. To bring the object to rest, its final velocity will be 0. According to the Work-Energy Theorem, the work done on the object is equal to the change in its kinetic energy.
Initial kinetic energy (KE_initial) = 0.5 * m * v^2
Final kinetic energy (KE_final) = 0.5 * m * (0)^2 = 0
Work done (W) = Change in kinetic energy = KE_final – KE_initial
W = 0 – (0.5 * m * v^2)
W = -0.5 * m * v^2
The negative sign indicates that the work done is against the motion of the object, which is required to bring it to rest. Therefore, the amount of work that should be done on the object in order to bring it to rest is 0.5 * m * v^2.
Question:
Certain force acting on a 20 kg mass changes its velocity from 5 m s-1 to 2 m s-1. Calculate the work done by the force.
Concept in a Minute:
Work-Energy Theorem: The work done by a net force on an object is equal to the change in its kinetic energy. Kinetic energy is the energy an object possesses due to its motion, calculated as (1/2) * mass * velocity^2.
Explanation:
The work done by the force is equal to the change in the kinetic energy of the mass.
Initial kinetic energy (KEi) = (1/2) * m * vi^2
Final kinetic energy (KEf) = (1/2) * m * vf^2
Work done (W) = KEf – KEi
Given:
Mass (m) = 20 kg
Initial velocity (vi) = 5 m/s
Final velocity (vf) = 2 m/s
Calculate initial kinetic energy:
KEi = (1/2) * 20 kg * (5 m/s)^2
KEi = 10 kg * 25 m^2/s^2
KEi = 250 Joules
Calculate final kinetic energy:
KEf = (1/2) * 20 kg * (2 m/s)^2
KEf = 10 kg * 4 m^2/s^2
KEf = 40 Joules
Calculate work done:
W = KEf – KEi
W = 40 Joules – 250 Joules
W = -210 Joules
The work done by the force is -210 Joules. The negative sign indicates that the force is acting in the opposite direction to the motion of the object, causing it to slow down.
Question:
Find the energy in joules consumed in 10 hours by four devices of power 500 W each.
Concept in a Minute:
The key concepts needed are:
1. Power: The rate at which energy is transferred or converted. It is measured in Watts (W).
2. Energy: The capacity to do work. It is measured in Joules (J).
3. Relationship between Energy, Power, and Time: Energy = Power × Time.
4. Unit Conversion: Time needs to be converted to seconds for energy in Joules.
Explanation:
First, calculate the total power consumed by all four devices.
Total Power = Number of devices × Power of each device
Total Power = 4 × 500 W = 2000 W
Next, convert the time from hours to seconds.
Time in seconds = Time in hours × 60 minutes/hour × 60 seconds/minute
Time in seconds = 10 hours × 60 × 60 = 36000 seconds
Now, calculate the energy consumed using the formula:
Energy = Total Power × Time
Energy = 2000 W × 36000 seconds
Calculate the final energy value in Joules.
Energy = 72,000,000 Joules
Therefore, the energy consumed is 72,000,000 J.
Alternatively, we can express this in scientific notation: 7.2 × 10^7 J.
Question:
Look at the activity below. Reason out whether or not work is done in the light of your understanding of the term ‘work’.
Food grains are getting dried in the sun.
Concept in a Minute:
Work is done when a force causes displacement in the direction of the force. In physics, work is defined as the product of force and displacement in the direction of the force. Mathematically, Work (W) = Force (F) × displacement (d) × cos(theta), where theta is the angle between the force and displacement. If there is no displacement, or if the displacement is perpendicular to the force, then no work is done.
Explanation:
In the given activity, food grains are placed in the sun to dry. The sun’s rays provide heat energy, which causes the water content in the food grains to evaporate. However, there is no force being applied by the sun on the food grains that causes them to move or displace. The food grains remain stationary. Since there is no displacement of the food grains due to any applied force, no work is done on the food grains, despite the process of drying happening. Work, in the physics sense, requires a force to cause a movement over a distance.
Question:
Define average power.
Concept in a Minute:
Power is the rate at which work is done or energy is transferred. Average power is the total work done or energy transferred over a specific time interval, divided by that time interval.
Explanation:
Average power is defined as the total work done (W) divided by the total time taken (t) to do that work. Mathematically, it is expressed as:
Average Power (P_avg) = W / t
Alternatively, if we consider the change in energy (ΔE) during a process, average power can also be defined as the total energy transferred divided by the time interval:
Average Power (P_avg) = ΔE / t
This means that if an object does a certain amount of work over a period of time, its average power is that work distributed evenly over that entire time. It does not consider the instantaneous power, which can vary during the process. For example, if a motor lifts a weight of 100 Joules in 5 seconds, its average power is 100 J / 5 s = 20 Watts.
Question:
What is power?
Concept in a Minute:
Power is the rate at which work is done or energy is transferred. It involves understanding work (force applied over a distance) and energy (the capacity to do work). The key is the *time taken* to perform the work or transfer the energy.
Explanation:
Power is defined as the rate at which work is done. Mathematically, it is expressed as:
Power (P) = Work (W) / Time (t)
Alternatively, since work is also the transfer of energy, power can also be defined as the rate at which energy is transferred:
Power (P) = Energy (E) / Time (t)
The SI unit of power is the Watt (W), which is equivalent to one Joule per second (1 J/s). A higher power rating means that more work can be done or more energy can be transferred in the same amount of time, or the same amount of work can be done in less time. For example, a more powerful engine can accelerate a car faster because it can do more work on the car in a shorter period.
Question:
Look at the activity below. Reason out whether or not work is done in the light of your understanding of the term ‘work’.
A donkey is carrying a load on its back.
Concept in a Minute:
Work is done when a force causes displacement of an object in the direction of the force. The formula for work is Work = Force × Displacement × cos(θ), where θ is the angle between the force and displacement.
Explanation:
In this scenario, the donkey is carrying a load on its back. This means the donkey is applying an upward force to counteract the force of gravity pulling the load downwards. However, the displacement of the load is horizontal (as the donkey walks). The force applied by the donkey is vertical, and the displacement is horizontal. The angle between the upward force and the horizontal displacement is 90 degrees. Since cos(90°) = 0, the work done by the donkey on the load is zero. While the donkey exerts a force, this force does not cause any displacement in its own direction. Therefore, according to the physics definition of work, no work is done by the donkey on the load.
Question:
Write an expression for the work done when a force is acting on an object in the direction of its displacement.
Concept in a Minute:
Work done by a force is defined as the product of the magnitude of the force and the distance moved by the object in the direction of the force.
Explanation:
Work done (W) is a measure of energy transfer that occurs when an object is moved over a distance by an external force, at least part of which is applied in the direction of the displacement.
When the force (F) is acting on an object and the object undergoes a displacement (d) in the exact same direction as the force, the work done is calculated by multiplying the magnitude of the force by the magnitude of the displacement.
Mathematically, this can be expressed as:
W = F * d
Here, W represents the work done, F is the magnitude of the force, and d is the magnitude of the displacement. Both F and d are vectors, but in this specific scenario, their directions are the same, so we can use their magnitudes for calculation.
Question:
A lamp consumes 1000 J of electrical energy in 10 s. What is its power?
Concept in a Minute:
The concept required to solve this problem is the definition of power. Power is the rate at which energy is transferred or consumed. It is defined as the energy consumed or transferred per unit of time. The formula for power is:
Power (P) = Energy (E) / Time (t)
The standard unit for energy is Joules (J), and the standard unit for time is seconds (s). The standard unit for power is Watts (W), where 1 Watt is equal to 1 Joule per second.
Explanation:
The question provides us with the amount of electrical energy consumed by a lamp and the time taken for this consumption.
Energy consumed (E) = 1000 J
Time taken (t) = 10 s
We need to find the power of the lamp. Using the formula for power:
P = E / t
Substitute the given values into the formula:
P = 1000 J / 10 s
Calculate the result:
P = 100 W
Therefore, the power of the lamp is 100 Watts.
Question:
What is the kinetic energy of an object?
Concept in a Minute:
The kinetic energy of an object is the energy it possesses due to its motion. It depends on the object’s mass and its velocity. The formula for kinetic energy is KE = 1/2 * m * v^2, where m is the mass and v is the velocity.
Explanation:
Kinetic energy is the energy an object has because it is moving. Imagine a moving car or a flying bird – they both have kinetic energy. The faster an object moves, the more kinetic energy it has. Also, a heavier object moving at the same speed will have more kinetic energy than a lighter object. The exact amount of kinetic energy is calculated using the formula KE = 1/2 * m * v^2. Here, ‘m’ represents the mass of the object (how much matter it contains), and ‘v’ represents its velocity (how fast it is moving and in what direction, though for kinetic energy calculation, we only need the speed squared).
Question:
A person holds a bundle of hay over his head for 30 minutes and gets tired. Has he done some work or not? Justify your answer.
Concept in a Minute:
Work is done when a force causes displacement. Mathematically, Work (W) = Force (F) × Displacement (d) × cos(θ), where θ is the angle between the force and displacement. If there is no displacement, then no work is done, regardless of the force applied or the effort expended.
Explanation:
The person holds the bundle of hay over his head, applying an upward force against gravity. However, the bundle of hay remains stationary; there is no displacement of the hay from its initial position. Since displacement (d) is zero, the work done (W = F × 0 × cos(θ)) is zero, irrespective of the force applied or the time the person holds the bundle. The person might feel tired due to the muscular effort and energy expenditure, but in physics, work is defined only when a force causes a movement. Therefore, no physical work has been done.
Question:
Define 1 watt of power.
Concept in a Minute:
Power is the rate at which work is done or energy is transferred. It is measured in watts (W). The relationship between power (P), energy (E), and time (t) is P = E/t. Alternatively, power can be related to voltage (V), current (I), and resistance (R) using formulas like P = VI, P = I^2R, and P = V^2/R.
Explanation:
1 watt of power is defined as the rate of doing work or transferring energy. Specifically, 1 watt is equivalent to 1 joule of energy transferred or work done per second. Mathematically, this can be expressed as:
1 W = 1 J/s
This definition is derived from the fundamental formula for power:
Power = Work Done / Time Taken
or
Power = Energy Transferred / Time Taken
Therefore, if 1 joule of work is done or 1 joule of energy is transferred in 1 second, the power is 1 watt.
Question:
Look at the activity below. Reason out whether or not work is done in the light of your understanding of the term ‘work’.
A sailboat is moving due to wind energy.
Concept in a Minute:
Work is done when a force causes displacement in the direction of the force. The formula for work is W = F * d * cos(theta), where F is the force, d is the displacement, and theta is the angle between the force and displacement.
Explanation:
In the case of a sailboat moving due to wind energy, the wind exerts a force on the sails. This force causes the sailboat to move, meaning there is a displacement. Since the force exerted by the wind is causing the displacement of the sailboat, work is being done. The wind’s force has a component in the direction of the boat’s motion, even if the wind is not blowing perfectly in the direction the boat is moving (due to the angle of the sails). Therefore, work is done on the sailboat.
Question:
Define 1 J of work.
Concept in a Minute:
Work done is defined as the product of force and displacement. When a force causes an object to move, work is done on the object. The unit of work in the SI system is the Joule (J).
Explanation:
Work done is calculated by the formula:
Work (W) = Force (F) × Displacement (d)
To define 1 Joule (J) of work, we need to consider the units of force and displacement.
The SI unit of force is the Newton (N).
The SI unit of displacement is the meter (m).
Therefore, 1 Joule of work is done when a force of 1 Newton causes a displacement of 1 meter in the direction of the force.
In simpler terms, if you push an object with a force of 1 Newton and it moves exactly 1 meter because of your push, then you have done 1 Joule of work.
Question:
Look at the activity below. Reason out whether or not work is done in the light of your understanding of the term ‘work’.
Suma is swimming in a pond.
Concept in a Minute:
Work is done when a force causes a displacement in the direction of the force. The formula for work done is W = Fd cosθ, where F is the force applied, d is the displacement, and θ is the angle between the force and displacement.
Explanation:
In the given activity, Suma is swimming in a pond. To swim, Suma applies forces to propel herself forward through the water. These forces cause her body to move (displace) through the water. Since there is both a force applied by Suma and a resulting displacement in the direction of the force (or at least a component of it), work is being done. The water resists Suma’s motion, and she exerts force against it to overcome this resistance and move forward. Therefore, work is done.
Question:
Write an expression for the kinetic energy of an object.
Concept in a Minute:
Kinetic energy is the energy an object possesses due to its motion. It depends on the object’s mass and its velocity. The formula for kinetic energy is derived from the work-energy theorem.
Explanation:
The kinetic energy (KE) of an object is defined as the energy it has because of its motion. It is directly proportional to the mass (m) of the object and the square of its velocity (v). The mathematical expression for kinetic energy is given by the formula:
KE = 1/2 * m * v^2
Where:
KE is the kinetic energy, typically measured in Joules (J).
m is the mass of the object, typically measured in kilograms (kg).
v is the velocity of the object, typically measured in meters per second (m/s).
Question:
A battery lights a bulb. Describe the energy changes involved in the process.
Concept in a Minute:
Energy transformation, specifically from chemical energy to electrical energy and then to light and heat energy.
Explanation:
The battery stores chemical energy. When the battery is connected to the bulb, a chemical reaction occurs within the battery. This chemical reaction converts the stored chemical energy into electrical energy. The electrical energy then flows through the wires to the bulb. Inside the bulb, the electrical energy is converted into two forms: light energy (which makes the bulb glow) and heat energy (which makes the bulb warm). Thus, the energy transformation sequence is: Chemical Energy $\rightarrow$ Electrical Energy $\rightarrow$ Light Energy + Heat Energy.
Question:
A pair of bullocks exerts a force of 140 N on a plough. The field being ploughed is 15 m long. How much work is done in ploughing the length of the field?
Concept in a Minute:
Work done is defined as the product of the force applied to an object and the distance over which that force is applied. The formula for work done is W = F * d, where W is work done, F is the force applied, and d is the distance moved in the direction of the force. The SI unit of work is the Joule (J).
Explanation:
To calculate the work done, we need to identify the force exerted and the distance over which the force is applied.
Given:
Force exerted by the bullocks (F) = 140 N
Length of the field (distance) (d) = 15 m
Using the formula for work done, W = F * d:
W = 140 N * 15 m
W = 2100 J
Therefore, the work done in ploughing the length of the field is 2100 Joules.
Next Chapter: Circles
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