Question:
The velocity of a body moving in a straight line is increased by applying a constant force F,for some distance in the direction of the motion. Prove that the increase in the kinetic energy of the body is equal to the work done by the force on the body.
Answer:
Let s be the distance covered by the body moving in the direction of constant force F.
Work done by this force on the body,
W = Fs
If a is the acceleration produced in the body of mass m due to this constant force F and if its velocity changes from u to v,then
F=ma
and = 2 as or s =
From eqns.(i),(ii) and (iii),w = (ma)=-
Since - Final kinetic energy - initial kinetic energy
= increase in kinetic energy,
Work done,W = increase in kinetic energy.
Work and Energy
Q 1.
Name a machine that transforms muscular energy into useful mechanical work.
Q 2.
Two girls,each of weight 400 N,climb up a rope through a height of 8 m.We name one of the girls A and the other B.Girl A takes 20 s while B takes 50 s to accomplish this task.What is the power expended by each girl ?
Q 3.
What do the machines need for their working ?
Q 4.
How does the wind move the blades of a wind-mill ?
Q 5.
A body is thrown vertically upwards. Its velocity goes on decreasing. Write the change in kinetic energy when its velocity becomes zero.
Q 6.
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?
Q 7.
When is work done by a force zero ?
Q 8.
The mass of a ball A is double the mass of another ball B.The ball A moves at half the speed of the ball B.Calculate the ratio of the kinetic energy of A to the kinetic energy of B.
Q 9.
Flowing water can rotate a turbine.What type of energy is used up by the turbine ?
Q 10.
What type of energy is possessed by a cricket ball just before being caught by a fielder ?
Q 11.
What is the form of energy possessed by a running car?
Q 12.
A freely falling object eventually stops on reaching the ground.What happens to its kinetic energy ?
Q 13.
What is the work done by a constant force ?When is it positive,negative or zero ?
Q 14.
Define potential energy.Derive an expression for the potential energy of a body of mass m,at a height h above the surface of the Earth.
Q 15.
A boy of mass 50 kg runs up a staircase of 45 steps in 9 s.If the height of each step is 15 cm,find his power.Take g =
.
Q 16.
The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of energy? Why?
Q 17.
A force of 5 N is acting on an object.The object is displaced through 2 m in the direction of the force.[in Fig.].If the force acts all through the displacement,find the work done by the force.
Q 18.
An object of mass 15 kg is moving with a uniform velocity of 4 m/s.What is the kinetic energy possessed by the object ?
Q 19.
A 60 kg person climbs stairs of total height 20 m in 2 min.Calculate the power delivered.
Q 20.
Define average power.
Q 21.
Name two forms of mechanical energy.
Q 22.
A force of 7 N acts on an object. The displacement is, say 8 m, in the direction of the force. Let us take it that the force acts on the object through the displacement. What is the work done in this case?
Q 23.
Name the type of energy possessed by a raised hammer?
Q 24.
A man does 200 J of work in 10 s and a boy does 100 J of work in 4 s.(a) Who is delivering more power ?
(b) Find the ratio of the power delivered by the man to that delivered by the boy.
Q 25.
What are the various energy transformations that occur when you are riding a bicycle ?
Q 26.
A certain household has consumed 250 units of energy during a month.How much energy is this in joules ?
Q 27.
Name the device which converts electrical energy into mechanical energy.
Q 28.
What is the difference between potential energy and kinetic energy ?
Q 29.
Can a body have energy without having momentum ?
Q 30.
Is it possible to havfc a situation where mechanical energy (E) - potential energy (
) Is negative,i.e.,(E-
)< 0.
Q 31.
Can a body have energy without possessing momentum?
Q 32.
An object of mass m is raised from the the earth to an height of equal to the radius of the earth (R). Calculate the gain in potential energy by the object. Assume gravity of the earth is g.
Q 33.
A battery lights a bulb. Describe the energy changes involved in the process.
Q 34.
A mass of 10 kg is at a point A on a table. It is moved to a point B. If the line joining A and B is horizontal, what is the work done on the object by the gravitational force? Explain your answer.
Q 35.
The magnitude of momentum of a moving object is equal to its kinetic energy. What will be the velocity of the object considering SI units for the system?
Q 36.
What is mechanical energy? What are its types?
Q 37.
An object of mass 40 kg is raised to a height of 5 m above the ground. What is its potential energy? If the object is allowed to fall, find its kinetic energy when it is half-way down.
Q 38.
A body of mass 120 g is taken vertically upwards to reach the height of 5m. Calculate work done. (Take g = 10 m/s
2)
Q 39.
A coolie carries a load of 50 kg on his head and walks on a level road upto 100 m.What is the work done by him ?
Q 40.
Write an expression for the work done when a force is acting on an object in the direction of its displacement.
Q 41.
Define 1 J of work.
Q 42.
A battery lights a bulb.Describe the energy changes involved in the process
Q 43.
When is work done by a force positive ?
Q 44.
What are the units of work and energy ?
Q 45.
Why do some engines require fuels like petrol and diesel ?
Q 46.
When an arrow is shot from a bow,it has kinetic energy.From where does it get the kinetic energy ?
Q 47.
What do you understand by the term energy ? Give its scientific conception.
Q 48.
Name a few forms of energy and their transformation into each other.
Q 49.
Many people debate about whether there is a God,or what God is.Is God an individual personality,sitting up in heaven listening to and granting our requests,or is God simply all the energy that exists in the Universe,or is God simply nature or the laws of nature ?
Q 50.
The recent horrific storm surge flooding New Jersey and New York in US by Hurricane Sandy was almost prefectly predicted well in advance,but was more extreme than the average person might expect from a minimal hurricane.There is a metric that quantifies the energy of a storm based on how far out tropical-storm force winds extend from the centre,known as Integrated Kinetic Energy (IKE).
(i) What is Sandy’s ranking in terms of IKE among all the hurricanes witnessed so far?
(ii) What is the IKE of Sandy?
(iii) How was Sandy different from Hurricane Katrina ?
(iv) Which human value did Sandy generate among the people round the globe?
