Case Study Questions Class 11 Physics Chapter 6 Work, Energy And Power
CBSE Class 11 Case Study Questions Physics Work, Energy And Power. Important Case Study Questions for Class 11 Board Exam Students. Here we have arranged some Important Case Base Questions for students who are searching for Paragraph Based Questions Work, Energy And Power.
At Case Study Questions there will given a Paragraph. In where some Important Questions will made on that respective Case Based Study. There will various types of marks will given 1 marks, 2 marks, 3 marks, 4 marks.
CBSE Case Study Questions Class 11 Physics Work, Energy And Power
Case Study – 1
1) The scalar product or dot product of any two vectors A and B, denoted as A.B (read A dot B) is defined as
A.B = A B cosθ
Where q is the angle between the two vectors. Since A, B and cosθ are scalars, the dot product of A and B is a scalar quantity. Each vector, A and B, has a direction but their scalar product does not have a direction. Following are properties of dot product
- the scalar product follows the commutative law : A.B = B.A
- Scalar product obeys the distributive law: (B + C) = A.B + A.C Further, A. (λ B) = λ (A.B) where λ is a real number.
- For unit vectors i, j, k we have
i × i = j × j = k × k = 1 and i × j = j × k = k × i = 0
- A×A = |A ||A| cos 0 = A2.
- B = 0, if A and B are perpendicular.
The work done by the force is defined to be the product of component of the force in the direction of the displacement and the magnitude of this displacement. Thus
W = (F cosθ )d = F.d ( We see that if there is no displacement, there is no work done even if the force is large. Work has only magnitude and no direction. Its SI unit is (N m) or joule (J). Thus, When you push hard against a rigid brick wall, the force you exert on the wall does not work.
No work is done if:
- The displacement is zero.
- The force is zero. A block moving on a smooth horizontal table is not acted upon by Horizontal force (since there is no friction), but may undergo a large displacement.
- The force and displacement are mutually perpendicular. This is so since, for θ = π/2 rad
- Cos (π/2) = 0. For the block moving on a smooth horizontal table, the gravitational force mg does no work since it acts at right angles to the displacement. If we assume that the moon’s orbits around the earth are perfectly circular then the earth’s gravitational force does no work. The moon’s instantaneous displacement is tangential while the earth’s force is radially inwards and θ = π/2.
1) Scalar product A.B = B.A is
a) commutative law
b) distributive law
c) both a and b
d) None of these
2) When force acts in the direction of displacement then work done will be
a) positive
b) negative
c) both a and b can possible
d) None of these
3) Define scalar product. give its properties
4)Define work done. Give its SI unit
5) Write down the conditions for which work done is zero
Answer key-1
1) a
2) a
3) The scalar product or dot product of any two vectors A and B, denoted as A.B (read A dot B) is defined as
A.B = A B cos q. where q is the angle between the two vectors. Since A, B and cosθ are scalars, the dot product of A and B is a scalar quantity. Each vector, A and B, has a direction but their scalar product does not have a direction. Following are properties of dot product
- the scalar product follows the commutative law :
A.B = B.A
- Scalar product obeys the distributive law:
(B + C) = A.B + A.C
Further, A. (λ B) = λ (A.B) where λ is a real number.
- For unit vectors i, j, k we have
i × i = j × j = k × k = 1 and i × j = j × k = k × i = 0
- A×A = |A ||A| cos 0 = A2.
- B = 0, if A and B are perpendicular.
4) The work done by the force is defined to be the product of component of the force in the direction of the displacement and the magnitude of this displacement. Thus
W = (F cosθ)d = F.d
Work has only magnitude and no direction. Its SI unit is (N m) or joule (J).
5) No work is done if :
- The displacement is zero.
- The force is zero. A block moving on a smooth horizontal table is not acted upon by a Horizontal force (since there is no friction), but may undergo a large displacement.
- The force and displacement are mutually perpendicular. This is so since, for θ = π/2 rad Cos (π/2) = 0.
Case Study – 2
The kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is
Kinetic energy is a scalar quantity. The kinetic energy of an object is a measure of the work and The energy possessed by an object is thus measured in terms of its capacity of doing work. The unit of energy is, therefore, the same as that of work, that is, joule (J).
Work energy theorem: The change in kinetic energy of a particle is equal to the work done on it by the net force. Mathematically
Kf – Ki = W
Where Ki and Kf are respectively the initial and final kinetic energies of the object. Work refers to the force and the displacement over which it acts. Work is done by a force on the body over a certain displacement.
1) Kinetic energy is
a) Scalar quantity
b) Vector quantity
c) None of these
2) Which of the following has same unit?
a) Potential energy and work
b) Kinetic energy and work
c) Force and weight
d) All of the above
3) What is work energy theorem?
4) Kinetic energy is scalar quantity. Justify the statement.
5) Give formula for kinetic energy of body.
Answer key-2
1) a
2) d
3) Work energy theorem: The change in kinetic energy of a particle is equal to the work done on it by the net force. Mathematically
Kf – Ki = W
Where Ki and Kf are respectively the initial and final kinetic energies of the object. Work refers to the force and the displacement over which it acts. Work is done by a force on the body over a certain displacement. Energy possessed by object due to its motion is called as kinetic energy. Its SI unit is N-m or Joule (J).
4) Kinetic energy is scalar quantity as it is a work done and work done is scalar quantity hence kinetic energy is also scalar quantity and doesn’t have any direction.
5) The kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is
Kinetic energy is a scalar quantity. Having unit the same as that of work, that is, joule (J).
Case Study – 3
The gravitational potential energy of an object at a point above the ground is defined as the work done in raising it from the ground by height h to that point against gravity. Let the work done on the object against gravity be W. That is, work done,
W = force × displacement
= mg × h
Therefore potential energy (PE) = mg*h. The dimensions of potential energy are [ML2T-2] and the unit is joule (J), the same as kinetic energy or work. To reiterate, the change in potential energy, for a conservative force, ΔV is equal to the negative of the work done by the force ΔV = − F(x) Δx.
Conservation of mechanical energy: Suppose that a body undergoes displacement Δx under the action of a conservative force F. Then from the WE theorem we have, ΔK = F(x) Δx
If the force is conservative, the potential energy function V(x) can be defined such that
− ΔV = F(x) Δx
The above equations imply that ΔK + ΔV = 0 or Δ (K + V) = 0.
Which means that K + V, the sum of the kinetic and potential energies of the body is a constant? Over the whole path, xi to xf, this means that Ki + V(xi ) = Kf + V(xf ). The quantity K +V(x), is called the total mechanical energy of the system. Individually the kinetic energy K and the potential energy V(x) may vary from point to point, but the sum is a constant. The aptness of the term ‘conservative force’ is now clear.
Let us consider some of the definitions of a conservative force.
- A force F(x) is conservative if it can be derived from a scalar quantity V(x).
- The work done by the conservative force depends only on the end points. This can be seen from the relation, W = Kf – Ki = V (xi ) – V(xf ) which depends on the end points.
- A third definition states that the work done by this force in a closed path is zero. This is once again apparent since xi = xf .
Thus, the principle of conservation of total mechanical energy can be stated as the total mechanical energy of a system is conserved if the forces, doing work on it, are conservative.
1) Dimensions of potential energy is given by
a) [ML2T-2]
b) [M2 L2T-2]
c) [ML3T-3]
d) None of the above
2) SI unit of potential energy is
a) Joule(J)
b) Newton meter(N-m)
c) both a and b
d) None of these
3) Define the gravitational potential energy.
4) Define conservative force
5) State conservation of mechanical energy
Answer key-3
1) a
2) c
3) The gravitational potential energy of an object at a point above the ground is defined as the work done in raising it from the ground by height h to that point against gravity. Let the work done on the object against gravity be W. That is, work done,
W = force × displacement
= mg × h
Therefore potential energy (PE) = mg*h. The dimensions of potential energy are [ML2T-2] and the unit is joule (J), the same as kinetic energy or work.
4) Let us consider some of the definitions of a conservative force.
- A force F(x) is conservative if it can be derived from a scalar quantity V(x).
- The work done by the conservative force depends only on the end points. This can be seen from the relation, W = Kf – Ki = V (xi ) – V(xf ) which depends on the end points.
- A third definition states that the work done by this force in a closed path is zero. This is once again apparent since xi = xf.
5) Conservation of mechanical energy:
Suppose that a body undergoes displacement Δx under the action of a conservative force F. Then from the WE theorem we have,
ΔK = F(x) Δx. If the force is conservative, the potential energy function V(x) can be defined such that − ΔV = F(x) Δx. The above equations imply that
ΔK + ΔV = 0 or Δ(K + V ) = 0.
Which means that K + V, Over the whole path, xi to xf, this means that
Ki + V(xi ) = Kf + V(xf ). The quantity K +V(x), is called the total mechanical energy of the system. Individually the kinetic energy K and the potential energy V(x) may vary from point to point, but the sum is a constant.
Case Study – 4
The impact and deformation during collision may generate heat and sound. Part of the initial kinetic energy is transformed into other forms of energy. A useful way to visualize the deformation during collision is in terms of a ‘compressed spring’. If the ‘spring’ connecting the two masses regains its original shape without loss in energy, then the initial kinetic energy is equal to the final kinetic energy but the kinetic energy during the collision time Δt is not constant. Such a collision is called an elastic collision. On the other hand the deformation may not be relieved and the two bodies could move together after the collision. A collision in which the two particles move together after the collision is called a completely inelastic collision. The intermediate case where the deformation is partly relieved and some of the initial kinetic energy is lost is more common and is appropriately called an inelastic collision. If the initial velocities and final velocities of both the bodies are along the same straight line, then it is called a one-dimensional collision, or head-on collision.
When two equal masses undergo a glancing elastic collision with one of them at rest, after the collision, they will move at right angles to each other.
1) After collision when two particles moves together then collision is
a) Elastic collision
b) Completely inelastic collision
c) Both a and b
d) None of these
2) In elastic collision, loss in kinetic energy is
a) Zero
b) Positive
c) Negative
d) None of these
3) What is head on collision?
4) What is elastic collision?
5) What is inelastic collision?
Answer key – 4
1) B
2) A
3) If the initial velocities and final velocities of both the bodies are along the same straight line, then it is called a one-dimensional collision, or head-on collision. In the case of small spherical bodies, this is possible if the direction of travel of body 1 passes through the centre of body 2 which is at rest. In general, the collision is two dimensional, where the initial velocities and the final velocities lie in a plane.
4) Elastic collision is the type of collision in which initial kinetic energy and final kinetic energy of system remains same that is net loss in kinetic energy is zero.
5) Inelastic collision is the type of collision in which initial kinetic energy and final kinetic energy of system does not remain same that is there is net loss in kinetic energy.
Case Study – 5
Power is defined as the time rate at which work is done or energy is transferred. The average power of a force is defined as the ratio of the work, W, to the total time t taken
Pav = W/t
The instantaneous power is defined as the limiting value of the average power as time interval approaches zero.
P = dw/dt
The work dW done by a force F for a displacement dr is dW = F.dr. The instantaneous power can also be expressed as
P = F.dr/dt
P = F.v
Where v is the instantaneous velocity when the force is F. Power, like work and energy, is a scalar quantity. Its dimensions are [ML2 T-3]. In the SI, its unit is called a watt (W). The watt is 1 J s-1. The unit of power is named after James Watt, one of the innovators of the steam engine in the eighteenth century. There is another unit of power, namely the horse-power (hp)
1 hp = 746 W
This unit is still used to describe the output of automobiles, motorbikes.
1) the time rate at which work is done or energy is transferred is called as
a) Energy
b) Force
c) Power
d) None of these
2) Limiting value of power as time interval approaches zero is called as
a) Average power
b) Instantaneous power
c) Both a and b
d) None of these
3) Power is directly proportional to
a) force
b) velocity
c) Both
d) None of these
4) Define instantaneous power. Give its SI unit and dimensions.
5) 1 horse power is equal to how many watt?
Answer key-5
1) c
2) b
3) c
4) The instantaneous power is defined as the limiting value of the average power as time interval approaches zero.
P = dw / dt
The work dW done by a force F for a displacement dr is dW = F.dr. The instantaneous power can also be expressed as
P = F.dr/dt
P = F.v
Where v is the instantaneous velocity when the force is F. Power, like work and energy, is a scalar quantity. Its dimensions are [ML2 T-3]. In the SI, its unit is called a watt (W).
5) 1 horse power is equal to 746 watt.