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Force = 7 N
Displacement = 8 m
Work done = Force × Displacement
W = F × S
W = 7 × 8
= 56 Nm
= 56 J
Therefore, work done is 56 J.
A work is said to be done when a force is applied on a body and makes the body move then we said work is done.
When a force is acting on a body in the direction of the applied force, then the work done on the body is given by the expression:
Work done = Force × Displacement
W = F × s
1 J is defined as the amount of work done when a force of one newton is applied over a displacement of one meter.
Applied force, F = 140 N
Displacement, d = 15 m
Work done = force x displacement
W = 140 × 15 = 2100 J
Work done is 2100 J.
The energy of a body due to its motion is known as kinetic energy. It is a scalar quantity, i.e it does not depend on direction.
Kinetic energy possessed by a body of mass m is moving with a uniform velocity v, is given by the expression,
Its SI unit is Joule (J).
Mass of the object = m
Velocity of the object = v = 5 m/s
Kinetic energy, EK = 25 J
(i) If the velocity of an object is doubled, then v = 5 × 2 = 10 m/s
Therefore, its kinetic energy becomes 4 times because it is proportional to the square of the velocity. Hence, kinetic energy = 25 × 4 = 100 J.
(ii) If velocity is increased three times, then its kinetic energy becomes 9 times because it is proportional to the square of the velocity. Hence, kinetic energy = 25 × 9 = 225 J.
Power is the amount of work done per unit time. It is a scalar quantity.
It is expressed in watt (W).
1 watt of power is defined as the power produced when 1 joule of work is done for 1 second
Energy consumed by the lamp ( work done ) = 1000 J
Time = 10 s
The average power is defined as the ratio of total work done and the total time taken.
Work is done whenever the given two conditions are satisfied:
(i) Force is applied.
(ii) Displacement takes place.
(iii) The angle between the force and displacement is not 90 degrees .
(a) When Suma is swimming in a swimming pool, she applies force in forward direction and moves in the forward direction. So, displacement is in the forward direction. Both are in the same direction. Therefore, work is done.
(b) When a donkey is carrying a load on his back, it is applied a force in the upward direction. But, displacement of the load is in the forward direction. Since, displacement is perpendicular to force, the work done is zero.
(c) When a wind-mill is lifting water from a well, it is applying a force in the upward direction and it is moving water in an upward direction. Hence, work is done by the wind-mill in lifting water from the well.
(d) In this case, there is no force involved when a green plant is carrying photosynthesis.
Therefore, the work done is zero.
(e) When an engine is pulling a train, it is applying a force in the forward direction. This allows the train to move in the forward direction. Hence, there is a displacement in the train in the same direction. Therefore, work is done by the engine on the train.
(f) When food grains are getting dried in the Sun, there is no force involved. Hence, the work done is zero during the process of food grains getting dried in the Sun.
(g) When a sailboat is moving due to wind energy, force is applied by the boat in the forward direction. Therefore, there is a displacement in the boat in the direction of force. Hence, work is done by wind on the boat.
Vertical displacement = h = 5 m
Mass of the object = m = 40 kg
Acceleration due to gravity = g = 9.8 m/s
Gravitational potential energy is given by the expression,
W = mgh
∴ W = 40 × 9.8 × 5 = 1960 J.
At half-way down, the potential energy of the object will be 1960 / 2 = 980 J.
Work is done whenever the given conditions are satisfied:
(i) Force is applied.
(ii) Displacement takes place.
(iii) The angle between the force and displacement is not 90 degrees.
When a satellite moves around the Earth, then the direction of force of gravity on the satellite is perpendicular to its displacement. Therefore , the work done on the satellite by the Earth is zero.
Yes. There can be displacement of an object in the absence of any force acting on it, for a uniformly moving object. Suppose an object is moving with uniform velocity. Force will be zero when acceleration is zero. Hence, there can be a displacement without a force.
Work is done whenever the given conditions are satisfied:
(i) Force is applied.
(ii) Displacement takes place.
(iii) The angle between the force and displacement is not 90 degrees.
When a person holds a bundle of hay over his head, then the bundle of hay remains stationary. Although, force of gravity is acting on the bundle, the person is not applying any force on it. Hence, in the absence of force, work done by the person on the bundle is zero.
Power of the heater, P = 1500 W = 1.5 kW
Time taken, T = 10 h
Energy consumed by an electric heater can be obtained with the help of the expression,
Power = Energy consumed / time
Therefore, Energy consumed = Power × Time
= 1.5 × 10 = 15 kWh
Hence, the energy consumed by the heater in 10 h is 15 kWh.
The law of conservation of energy states that energy can neither be created nor be destroyed. It can change from one form to another. Consider the case of an oscillating pendulum.
When a pendulum moves from its mean position P to either of its extreme positions A or B, it rises through a height h above the mean level P. At this point, the kinetic energy of the bob changes completely into potential energy. The kinetic energy becomes zero, and the bob possesses only potential energy. As it moves towards point P, its potential energy decreases progressively. Accordingly, the kinetic energy increases. As the bob reaches point P, its potential energy becomes zero and the bob possesses only kinetic energy. This process is repeated as long as the pendulum oscillates.
The bob does not oscillate forever. It comes to rest because air resistance resists its motion. The pendulum loses its kinetic energy to overcome this friction and stops after some time.
The law of conservation of energy is not violated because the energy lost by the pendulum to overcome friction is gained by its surroundings. Hence, the total energy of the pendulum and the surrounding system remain conserved.
Mass of the object = m
Velocity = v
Therefore ,Kinetic energy
amount of work is required to be done on the object.Mass of car, m = 1500 kg
Velocity of car, v = 60 km/h
Therefore, Kinetic energy
Work is done whenever the given conditions are satisfied:
(i) Force is applied.
(ii) Displacement takes place.
(iii) The angle between the force and displacement is not 90 degrees .
Case I
In this case, the angle between the force and displacement is 90 degrees. Hence, work done by force on the block will be zero.
Case II
In this case, the angle between the force and displacement is 0 degree. Hence, work done by force on the block will be positive.
Case III
In this case, the angle between the force and displacement is 180 degrees. Hence, work done by force on the block will be negative.
Yes, I agree with Soni that acceleration in an object could be zero even when several forces are acting on it. This happens when equal and opposite forces act on an object, they cancel out each other so that the net external force experienced by the object is zero. Therefore, the acceleration of the object is zero. Therefore, Soni is right.
There is no work done because the applied force is in the vertical direction but the displacement of the body is in the horizontal direction. Since the angle between force and displacement is 90 degrees.
Power of one device, P = 500 W = 500 / 1000 = 0.50 kW
Power of four devices = 500 x 4 = 2000 W = 2000 / 1000 = 2 kW
Time taken, T = 10 h
We know that
Power = energy consumed / time
Energy consumed = Power × Time
= 2 × 10 = 20 kWh
Therefore, the energy consumed by four equal rating devices in 10 h will be 20 kWh.
When an object falls freely towards the ground, its potential energy decreases and kinetic energy increases. When a free falling object hits the ground, its kinetic energy becomes zero and its potential energy becomes maximum. The kinetic energy changes into heat and sound energy while the object comes to rest.
When a battery lights a bulb , then the chemical energy of the battery is transferred into electrical energy. When the bulb receives this electrical energy, then it converts it into light and heat energy. Therefore, energy changes are shown as :
Mass of the body = 20 kg
Initial velocity, u = 5 m/s
Final velocity, v = 2 m/s
Kinetic energy is given by the expression,
(i) Kinetic energy when the object was moving with a velocity 5 m/s
(ii) Kinetic energy when the object was moving with a velocity 2 m/s
Work done = change in kinetic energy.
Therefore, work done = (Ek)2 - (Ek)5
= 40 − 250 = −210 J
The negative sign indicates that the force is acting in the direction opposite to the motion of the object.
There is no work done because the force is gravitational force which is in downward direction but the displacement of the body is in horizontal direction. Since the angle between force and displacement is 90 degrees.
No. The process does not violate the law of conservation of energy. This is because when the body falls from a height, then it loses its potential energy. But as it falls, it gains some velocity. Due to increase in velocity, the body gains kinetic energy. During the process, total mechanical energy of the body remains conserved. Hence, the law of conservation of energy is not violated.
While riding a bicycle, we use our muscular energy to make the cycle move and our body also warms up in the process. Therefore, the muscular energy gets converted into kinetic energy and heat energy. The energy transformation can be shown as:
When we push a huge rock, we apply muscular force in order to move it. There is no transfer of muscular energy to the stationary rock. Also, there is no loss of energy because muscular energy is converted into heat energy, which causes our body to feel warm.
1 unit of energy = 1 kilowatt hour (kWh)
1 kWh = 3.6 × 106 J
Therefore, 250 units of energy = 250 × 3.6 × 106 = 9 × 108 J
Let the initial velocity of rocket = v, the new velocity when suddenly tripled = 3v
Let the mass of the rocket be m
Initial kinetic energy = final kinetic energy
1/2 mv^2 = 1/2 m (3v)^2 => 1: 9
We know that
Power = Force x Velocity
∴ Power of Avinash, PA = 10 N x 8 m/s = 80 W
Power of Kapil, PK= 25 N x 3 m/s = 75 W
PA > PK
So, Avinash is more powerful than Kapil.
Frictional force, F = 5 N
∴ Work done by boy = Force x Total distance covered
Total distance covered =1.5km + 1.5km ( 2π x 100 m ) + 2km = 1500 + 1500(2π + 100) + 2000 = 1500 + 942 + 2000 = 4442 m (4.442 km)
= 5 N × 4.442 km
= 5 N × 4442m = 22210J
Momentum of a body is equal to the product of its mass and velocity. It is given that, momentum of the body is zero, it means the velocity of the body is zero. But mechanical energy is the sum of kinetic energy and potential energy. So the kinetic energy of a body is equal to zero. But it may have potential energy. So, even if the momentum of the body is zero, it may have mechanical energy.
If an object has momentum it must have a kinetic energy but mechanical energy is the sum of potential and kinetic energy. So if the datum (the level from which the height of an object is measured) is taken above the object then the object can have negative potential energy equal in magnitude to kinetic so that their addition (mechanical energy) is zero.
Power of pump = 2kW = 2000 W
Height, h = 10 m, time (t) = 60 sec, g = 10m/s^2
We know that, Power = work done per unit time (mgh) / time
2000 = (m x 10 x 10) / 60 => m = (2000 x 60) / 100
M = 1200 kg
Hence the pump can raise 1200 kg of water in one minute.
The potential energy of a person will remain the same on the earth and on planet A
Potential energy = mgh
mg1h1 = mg2h2 (g1 = g, g2 = ½ g & h1 = 0.4 m)
Now, h2 = g1h1/g2 => g x 0.4 / (g/2) = 0.8 m.
Let a body of mass changes its velocity from "u" to "v" with an acceleration, "a" due to the application of a constant force, "F" in the direction of motion, then the displacement of the body, "S" is given by ⇒S = (v2 - u2)/2a, but the work done in changing the velocity of the body from u to v is W = F.S
W = ma[(v2 - u2)/2a]
W = m[(v2 - u2)/2]
W = m/2[v2 - u2]
W = m/2(v2) - m/2(u2)
W = 1/2(mv2) - 1/2(mu2),
But 1/2(mv2) - 1/2(mu2) = Change in kinetic energy So, Change in kinetic energy = W = 1/2(mv2) - 1/2 (mu2).
Yes, it is possible that an object is in the state of accelerated motion due to external force acting on it, but no work is being done by the force.
For example, the earth is constantly moving in a circular path in a direction perpendicular to the gravitational pull of the Sun. So, the work done by the gravitational force is zero. Therefore the work done can be zero for an accelerated body.
Let the initial energy of the body of mass (m) at height (h) is mgh. If the energy of the ball reduces by 40 % after striking the ground, the remaining energy of the ball will be 60 % of initial energy.
According to the question,
mgh’ = 60% of mgh => h’ = (60/100) 10 = 6 m.
Power , P = 1200 W
Time (everyday), t = 30 min = 30 x 60 = 1800 sec.
Energy consumed in one day = P x t => 1200 x 1800
= 2.16 x 106 J
Energy consumed in the April month = 2.16 x 106 x 30 J
= 6.48 x 107 J
Momentum of a body, P = MV
Assume both the particles have mass M and m and have speed v and v’ respectively. Both the particles have same momentum (Mv = mv’)
Kinetic energy ,K.E = 1/2 Mv^2 = ½ (MxMx v^2)/M = (1/2) (p^2)/M
K.E’ = 1/2 mv’^2 = 1/2 (m x m x v’^2)/m = (1/2)(p^2)/m
K.E / K.E’ = (p^2/2M) / (p^2/2m) = 2m/2M = m/M
Since M>m
So, (m/M)<1 (K.E < K.E’)
Therefore, light particles have more kinetic energy than that of heavier particles.
Mass , (mA) = (mB) = 1000 kg
Initial speed , uA = 36 km / hr.
Opposing frictional force, F = 100 N
Since , the car A moves with a uniform speed , it means that the engine of car applies a force equal to the frictional force
∴ Power = ( Force x displacement ) / time
= F µA = (100 ) x (10 ) = 1000 W
After collision
Final speed of car A, vA = 0
Initial speed of car B, uB = 0
Using conservation of momentum, P, = P,
mAvA + mBuB = mAvA + mBvB
1000 x 10 + 1000 x 0 = 1000 x o + 1000 x vB
∴vB = 10m/s
Mass of girl = 35 kg, mass of trolley = 5kg
Total mass = 35 + 5 = 40 kg
Initial velocity, u = 4 m/s,
final velocity, v = 0,
distance, s = 16 m
Using equation, v^2 = u^2 + 2as
0 = (4)^2 + 2a (16) => 32a = - 16 => a = - 0.5 m/s^2
Force exerted by trolley, F = ma
= 40 x 0.5 = 20 N
(a) Work done on trolley, W = F.S => 20 x 16 = 320 J
(b) Work done by girl, W = F.S => mass of girl x retardation x S
= 35 x 0.5 x 16 = 280 J.
Mass of the box, m = 250 kg
Height, h = 1 m
Force, F = mg = 250 x 10 = 2500 N
(a) Work done by the men in lifting the box = F.S = 2500 x 1 = 2500 J
(b) Zero work is done , as the box does not move at all while holding it.
(c) The energy of man loses while applying the force and muscular effort is involved, In order to hold the box at a certain height. Due to loss of energy he felt tired.
Power is the rate of doing work.
Kilowatt is the unit of power and kilowatt hour is the unit of energy.
Mass = 2000 tones = (2000 x 10^3 kg = 2 x 10^6 kg)
Height = 20 m
Power, P = (mgh) / t
= (2 x 10^6 x 10 x 20) / 60 => (2/3) x 10^7 W
Power = 100 W
Speed = 1 m/s
g = 10 m/s^2 (given)
Power = (mgh) / t [Here (h/t) = speed]
1 watt is the power of an appliance which does work at the rate of 1 joule per second.
Watt is the S.I unit of Power.
Mass , m = 150 kg
Power developed by engine per kg = 500 W
Total power , P = 500 W x 150 = 75000 W
Speed of car, ( velocity ) v = 20 m/s
Power, P = Force x velocity
Force = Power / velocity
= (7.5 x 10^4) / 20 => 3.75 x 10^3
= 3750 N.
(i) Mass of butterfly = 1 g = 1/1000 kg
Speed, vb = 0.5 m/s
Power, Pb = m x g x vb = (1/1000) x 10 x 0.5 = 0.005 W
(ii) Mass of squirrel = 250 g = 250/1000 = 0.25 kg
Speed, vs = 0.5 m/s
Power, Ps = m x g x vs= 0.25 x 10 x 0.5 = 1.25 W
Therefore, the power with which the squirrel is climbing is much higher than that of a butterfly flying.
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