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Question (1):
List out the conditions to be satisfied for work to be done.
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Answer:
The conditions to be satisfied for work to be done are:
 Some force must act on the object
 The point of application of the force must move
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Question (2):
Define kinetic energy.
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Answer:
Kinetic energy is the energy possessed by an object by virtue of its motion.
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Question (3):
How is work measured?
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Answer:
Work is measured by the product of the force and the distance covered.
i.e., W = F x S
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Question (4):
What kind of energy transformation takes place in a toy bus driven by a winding key?
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Answer:
In a toy bus driven by a winding key potential energy of the wound spring is transformed into kinetic energy.
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Question (5):
Name two forms of mechanical energy.
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Answer:
The two forms of mechanical energy are potential energy and kinetic energy.
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Question (6):
Flowing water can rotate a turbine. Which type of energy does the turbine use?
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Answer:
The turbine uses the kinetic energy of flowing water.
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Question (7):
Define potential energy.
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Answer:
Potential energy is the energy possessed by an object by virtue of its position or condition.
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Question (8):
Define power.
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Answer:
Power is the rate of doing work.
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Question (9):
Name the two factors on which the kinetic energy of a body depends.
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Answer:
Kinetic energy of a body depends on its mass and its velocity.
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Question (10):
State the law of conservation of energy.
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Answer:
Energy can neither be created nor destroyed but can be transformed from one form to another.
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Question (11):
What kind of energy transformation takes place in an electric fan and in a loudspeaker?
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Answer:
In an electric fan electrical energy is transformed into mechanical energy and in loudspeaker the electrical energy is converted into sound energy.
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Question (12):
What will be the change in kinetic energy of a body when its speed is halved?
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Answer:
Where m is the mass of the object and v is the velocity of the object.
Let T1 be the kinetic energy of the body when its speed is halved.
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Question (13):
Show that  where the symbols have their usual meaning.
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Answer:
Substituting the value of v in equation (1), we get
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Question (14):
Which type of energy is possessed by a wound spring of a watch?
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Answer:
The wound spring of a watch possesses potential energy.
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Question (15):
Power is defined as the rate of doing work. Show that power can also be defined as the product of force and velocity.
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Answer:
W = F x S
Substituting for W in equation 1 we get,
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Question (16):
A body of mass 2 kg is dropped form the top of a tower of height 100 m. What will be its kinetic energy at the end of 2 seconds? Given g = 10m/s2.
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Answer:
Mass of the body = 2kg
v = ?
Initial velocity (u) = 0
We have to calculate velocity at the end of 2 seconds. v is calculated from the first equation of motion.
v = u + gt
v = 0 + 9.8 x 2
v = 19.6 m/s
Kinetic energy at the end of two seconds = 384.16 J
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Question (17):
A horse and a dog are running with the same speed. If the weight of the horse is ten times that of the dog, what is the ratio of their kinetic energies?
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Answer:
Let v be the velocity with which dog and horse are running.
Given :
Mass of the horse = 10 times mass of the dog
Let 'm' be the mass of the dog.
Then,
Mass of horse = 10m
Ratio of kinetic energies = 1:10
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Question (18):
Calculate the kinetic energy of a ball of mass 10 g and momentum 1000 g cm/s.
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Answer:
Momentum of the ball = 1000 g cm/s
= 0.01 kgm/s
Kinetic energy = 0.005 J
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Question (19):
Name a gadget where the following transformation of energies take place.
a) Chemical energy to electrical energy
b) Electrical energy to mechanical energy
c) Electrical energy to heat and light
d) Electrical energy to sound energy
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Answer:
 Chemical energy to electrical energy - torch
 Electrical energy to mechanical energy - electric fan
 Electrical energy to heat and light - electric bulb
 Electrical energy to sound energy - loud speaker
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Question (20):
State the factors on which the potential energy of a body depends.
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Answer:
The potential energy of a body depends on
 the height from the ground
 acceleration due to gravity at that place
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Question (21):
State the law of conservation of energy. Explain the law by taking oscillating simple pendulum as an example.
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Answer:
The law of conservation of energy states that energy can neither be created nor destroyed but can be transformed from one form to another.
In the case of a simple pendulum when the bob is at the extreme left, it has the maximum potential energy, as it is raised with respect to the mean position. But its kinetic energy is zero as the bob stops oscillating for a fraction of a second before moving towards the right.
When the bob reaches the mean position, it has a zero potential energy but maximum kinetic energy.
Similarly when the bob of the pendulum swings to extreme right, it has the maximum potential energy but zero kinetic energy. Thus, law of conservation of energy holds good in the case of an oscillating pendulum.
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Question (22):
The figure shows the simple pendulum, which starts oscillating from the extreme position A. Show that the speed of the pendulum when it passes the mean position B is  where 'h' is the distance through which the bob of the pendulum is displaced from the mean position.
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Answer:
When the pendulum is at A it possesses potential energy and the initial velocity is zero. The pendulum attains maximum velocity at the mean position.
We make use of the III equation of motion.
Here, u = 0, a = g and S = h
 The speed of the pendulum as it passes the mean position is 
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Question (23):
How fast should a man of mass 50 kg run, so that his kinetic energy is 625 J?
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Answer:
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Question (24):
Two bodies of equal mass are kept at a height of 'h' and '3h'. What is the ratio of their gravitational potential energies?
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Answer:
Potential energy (P.E.) = mgh
P.E. (1) = mgh
P.E. (2) = mg3h
\ P.E. (1) : P.E. (2) = 1 : 3
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Question (25):
A boy spends 800 J of energy while lifting a body of mass 40 kg from a well. Calculate the depth of the well. Given g = 10 m/s2.
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Answer:
The energy spent is equal to potential energy as the object is lifted through a certain height.
Potential energy = 800 J
Mass of body lifted (m) = 40 kg
Potential energy = mgh
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Question (26):
A nail becomes warm when it is hammered into a plank. Explain why.
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Answer:
A raised hammer has potential energy due to its position above the ground. When the hammer comes down and strikes the head of the nail, the potential energy is transformed into kinetic energy. If we continue hitting the nail to secure it, the kinetic energy of the hammer is transferred to the molecules of the material of the nail. The heat content of the body is the total energy that the body possesses. Hence, as the heat content of the body increases, the nail becomes warm.
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Question (27):
Calculate the height of a building if 20,000 J of energy is required to lift 200 kg of water from a well to a tank on the top of the building. Given g = 10 m/s2.
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Answer:
Work done in lifting water = potential energy = mgh
Mass of water (m) = 200 kg
g = 10 m/s2
Potential energy = 20,000 J
= 10 m
Height of the building = 10 m
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Question (28):
Define potential energy and derive an expression for it.
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Answer:
Potential energy of an object can be defined as the energy possessed by the object by virtue of its position or condition.
Expression for potential energy
Consider an object of mass 'm', raised through a height 'h' above the earth's surface. The work done against gravity gets stored in the object as its potential energy.
Therefore, potential energy = work done in raising the object through a height 'h'
Potential energy = F x S ...(1)
But F = mg (according to Newton's second law of motion)
S = h
Substituting for F and S in equation 1, we get
Potential energy = mgh< |
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Question (29):
a) State law of conservation of energy.
b) A stone of mass 10 g placed at the top of a tower 50 m high is allowed to fall freely. Show that law of conservation of energy holds good in the case of the stone.
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Answer:
a) Energy can neither be created nor destroyed but can be transformed from one form to another.
b)
In this case we have to prove that total energy at A, B and C is the same.
Height = 50 m
Potential energy at A = mgh
= 0.01 x 9.8 x 50
= 0.01 x 98 x 5
= 4.9 J
= 0
Total energy at A = potential energy + kinetic energy= 4.9 + 0
Total energy at A = 4.9 J ...(1)
At B
Height from the ground = 40 m
Potential energy = mgh
= 0.01 x 9.8 x 40
= 0.01 x 98 x 4
Potential energy at B = 3.92 J
To calculate v we make use of III equation of motion,
Here, u = 0, a = 9.8 m/s2 and S = 10 m
= 0.98 J
Total energy at B = potential energy + kinetic energy
= 3.92 + 0.98
Total energy at B = 4.90 J (2)
At C
Height from the ground = 0
Potential energy at C = mgh
To calculate v we use III equation of motion,
Here, u = 0, a = 9.8m/s2 and S = 50 m
= 4.9 J
Total energy at C = potential energy + kinetic energy
= 0 + 4.9
Total energy at C = 4.9 J (3)
The total energy at A, B and C is 4.9 J. This means that law of conservation of energy holds good in the case of a stone falling freely under gravity. |
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Question (30):
In hydroelectric power plant, water falls at a rate of 1000 kg/s from a height of 100 m. Assuming that 60% of the energy of falling water is converted into electrical energy, calculate the power generated per second.
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Answer:
Mass of water (m) =1000 kg
Height (h) =100 m
Energy possessed by water = potential energy = mgh
Total energy generated = 980000 J
Out of this total energy only 60% is converted to electrical energy.
= 588000 J
Time = 1 s
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Question (31):
A body is thrown vertically upwards. Its velocity keeps on decreasing. What happens to its kinetic energy when its velocity becomes zero?
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Answer:
The kinetic energy becomes zero. According to the law of conservation of energy the kinetic energy is converted into potential energy.
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Question (32):
An electric motor of power 100 W is used to drive the stirrer in a water bath. If 50% of the energy supplied to the motor is spent in stirring the water, calculate the work done on the water in one minute.
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Answer:
Power of the electric motor =100 W
Time = 1 minute
= 60 s
 Energy supplied by the motor = P x t
Only 50% of the energy is used for heating water.
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Question (33):
a) State law of conservation of energy.
b) A mass of 4 kg is dropped from a tower of height 45 m. Calculate
(i) the potential energy possessed by the body when it is at the top of the tower
(ii) the kinetic energy possessed by the body when it is at a height of 35 m
(iii) the kinetic energy just before hitting the ground
(iv) the velocity of the body just before hitting the ground.
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Answer:
a) Law of conservation of energy states that energy can neither be created nor destroyed but can be transformed from one form to another.
b) Mass of the body (m) = 4 kg
Height of the tower (h) = 45 m
Acceleration due to gravity = 9.8m/s2
i) Potential energy possessed by the body when it is at a height of 45 m above the ground = mgh
ii) Kinetic energy of a moving body when it is at a height of 35 m from the ground is equal to the kinetic energy possessed by the body after covering 10 m.
First we have to calculate the velocity with which the body covers 10 m.
iii) According to the law of conservation of energy the kinetic energy of the body just before hitting the ground is equal to potential energy of the body at a height of 45m above the ground.
 Kinetic energy of the body just before hitting the ground = 1764 J
Velocity = 29.69 m/s.
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Question (34):
Define energy. What is the SI unit of energy?
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Answer:
Energy is the capacity to do work.
The SI unit of energy is joule.
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Question (35):
Two bodies of equal mass move with uniform velocities v and 4 V. Find the ratio of their kinetic energies.
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Answer:
Let m be the mass of the bodies and T1 and T2 represent the kinetic energy of the bodies.
Ratio of kinetic energies = 1:16
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Question (36):
A boy pushes a cart through a distance of 150 m by applying a force of 50 N. Calculate the work done by the body.
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Answer:
Force applied (F) = 50 N
Distance covered (S)= 150 m
Work done (w) = F x S
Work done = 50 x 150
= 7500 J
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Question (37):
A pump is used to lift 1000 kg of water, through a vertical height of 10 m. Calculate the work done in operating the pump.
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Answer:
Mass of water (m) =1000 kg
Height through which water is lifted (h) =10 m
Acceleration due to gravity = 9.8 m/s2
Work done in operating the pump = F x S
F = mg (From Newton's II law of motion)
S = h
 Work done = mgh
= 98000 J
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Question (38):
Calculate the mass of a box, which is lifted vertically through a height of 25 m, if the work done in lifting it is 6250 J. (g = 10 m/s2)
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Answer:
Work done in lifting the box = 6250 J
The work done in lifting the box is stored in it as its potential energy.
W= potential energy = mgh
Mass of the box = ?
Height through which the box is lifted = 25 m.
Potential energy = 6250 J
Potential energy = mgh
6250 = m x 10 x 25
m 
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Question (39):
An engine supplies 15,000 J of energy in one minute. Calculate the power of the engine
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Answer:
Energy supplied by the engine =15000 J
Time = 1 minute
= 60 s
Power of the engine = 250 watts
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Question (40):
A crane lifts a mass 1-ton through a vertical height of 10 m in 25 s. Calculate the power of crane. Given g = 10 m/s2.
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Answer:
Mass (m) = 1 ton = 1000 kg
Height through which the mass is lifted h = 10 m
Time (t) = 25 s
Since the mass is lifted through a height 'h' it possesses potential energy.
 Power of the crane = 4000 W
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Question (41):
Calculate the time taken by a water pump of power 500 W to lift 2000 kg of water to a tank, which is at a height of 15 m from the ground?
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Answer:
Given g = 10 m/s2
Power of the water pump = 500 W
Since the water is lifted through a height of 15 m, work done is equal to the potential energy.
Mass of water (m) = 2000 kg
Height (h) = 15 m
t = ?
t = 40 x 15 = 600 s
Time required to lift water = 600 s
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Question (42):
A stone of mass 5 kg is lying at the edge of a cliff, which is 80 m above the ground. Calculate the energy possessed by the stone.
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Answer:
The stone possesses potential energy as it is kept at a height above the ground.
Mass of the stone (m) = 5 kg
Height (h) = 80 m
Potential energy of the stone = mgh
Potential energy of the stone = 3920 J
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Question (43):
For the same kinetic energy of a body, what should be the change in its velocity if its mass is increased four times?
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Answer:
Let 'm1' be the mass of a body moving with a velocity 'v1'.
When mass is increased four times let the velocity be v2.
v2 = ?
Substitute the value of m2 in the above equation
Given
The velocity of the body is halved when its mass is increased four times.
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Question (44):
The momentum of a body of mass 60 kg is 3000 kg m/s. Calculate the kinetic energy and speed of the body.
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Answer:
Expression for kinetic energy when momentum is given
Momentum of the body = 3000 kg m/s
Mass of the body = 60 kg
kinetic energy = 75000 J
Kinetic energy is given by the equation
Speed of the body = 50 m/s.
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Question (45):
How much energy does a 60 W bulb consume per second?
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Answer:
Power of the bulb = 60 W
Time = 1 s
Energy consumed by the bulb = P x t
= 60 x 1 = 60 joules
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Question (46):
Cricket and tennis balls have equal momentum. Which one will have more kinetic energy?
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Answer:
Let pc and pt be the momentum of the cricket and tennis ball respectively.
Given, pc = pt = p
\ From equations 1 and 2 it clear that tennis ball will have more kinetic energy.
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Question (47):
Show that the kinetic energy of a body dropped from a height 'h' on reaching the ground is equal to the potential energy of the body at the point from where it was dropped.
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Answer:
Let a body of mass 'm' be dropped from a height 'h' above the ground.
The potential energy of the body = mgh.
Initial velocity of the body (u) = 0.
'v' is the velocity with which the body covers a distance 'h'.
We make use of the III equation of motion to calculate the velocity 'v'
That is the kinetic energy of the body when it reaches the ground after travelling a height 'h' is equal to the potential energy of the body at height 'h'.
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Question (48):
Which would have a greater effect on the kinetic energy of an object -doubling the mass or doubling the velocity?
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Answer:
When the mass is doubled the kinetic energy is doubled. While when the velocity is doubled, the kinetic energy increases four times. Therefore, doubling the velocity will have a greater effect on the kinetic energy of an object.
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Question (49):
A man drops a 10 kg rock from the top of a 5 m ladder. What is its kinetic energy when it reaches the ground? What is its speed just before it hits the ground?
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Answer:
Mass (m) = 10 kg
Height (h) = 5 m
Potential energy at the top of a 5 m ladder = mgh
According to law of conservation of energy the potential energy is completely converted to kinetic energy when it reaches the ground.  Kinetic energy of the rock when it reaches the ground = 490 J
Speed of the rock = 9.89 m/s.
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Question (50):
A car weighing 1000 kg and travelling at 30 m/s stops at a distance of 50 m decelerating uniformly. What is the force exerted on it by the brakes? What is the work done by the brakes?
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Answer:
Mass of the car (m) = 1000 kg
Initial velocity (u) = 30 m/s
Distance traveled (S)= 50 m
Since the car stops, final velocity (v) = 0
Work done by the brakes = kinetic energy of the car
W = F x S
The force exerted by the brakes is 9000 N.
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Question (51):
Define kinetic energy and derive an expression for it.
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Answer:
Kinetic energy is defined as the energy possessed by an object by virtue of its motion.
Expression for kinetic energy.
Consider a body of mass 'm' which is initially at rest. When a force 'F' is applied on the body it starts moving with a velocity 'v' and covers a distance 'S'. The force produces acceleration 'a' in the body.
The force 'F' does work when it moves the body through a distance 'S' and this work done is stored in the body as its kinetic energy.
By definition,
W = F x S ... (1)
F = ma (According to Newton's second law of motion)
Substituting the value of 'F' in equation 1 we get
W = mas ...(2)
We get an expression for 'a' using the III equation of motion
Substituting the value of 'a' in equation (2), we get
But since work done is stored in the body as its kinetic energy, equation(3) can be
written as
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Question (52):
Define power. A boy of mass 45 kg runs up a flight of 100 steps, each measuring 20 cm, in one minute and 30 seconds. Calculate the power of the boy. Given g = 10 m/s2.
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Answer:
Power is defined as the rate of doing work.
Mass of the boy (m) = 45 kg
Vertical height (h) = number of steps x height of each step.
= 2000 cm = 20 m ( 1m = 100 cm)
Acceleration due to gravity (g) = 10 m/s2
Work done by the body against gravity = potential energy
= mgh
Time = 1 min and 30 s
Time = 60 + 30 = 90 s
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Question (53):
Show that law of conservation of energy holds good in the case of a freely falling body.
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Answer:
Let a body of mass 'm' placed at a height 'h' above the ground start falling down from rest.
At A,
Potential energy = mgh
 Total energy at A = Potential energy + kinetic energy.
= mgh + 0
Total energy at A = mgh (1)
At B,
Potential energy = mg(h - x) [Height from the ground is (h - x)]
 Potential energy = mgh - mgx
The body covers the distance 'x' with a velocity 'v'. We make use of the third equation of motion to obtain the velocity of the body.
Here u = 0, a = g and S = x
Kinetic energy = mgx
 Total energy at B = potential energy + kinetic energy
= mgh - mgx + mgx
 Total energy at B = mgh (2)
At C,
Potential energy = mgh [Since the body is on the ground h=0]
= 0
The freely falling body has covered the distance 'h'.
Here, u = 0, a = g and S = h
Kinetic energy = mgh
 Total energy at C = mgh (3)
It is clear from equation (1), (2) and (3) that the total energy of the body remains constant at every point. Thus, we conclude that law of conservation of energy holds good in the case of a freely falling body.
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