Physics Chapter on Kinetic Energy

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Questions and Answers

What is true about stable equilibrium?

The force acting on it pushes it further away.

The potential energy is at maximum.

The second derivative of potential energy is positive. (correct)

The potential energy is at minimum. (correct)

Which example represents an unstable equilibrium?

A marble at the bottom of a bowl.

A marble balanced on top of a hemispherical bowl. (correct)

A book resting flat on a table.

A pendulum hanging straight down.

In the context of equilibrium, what does a negative second derivative of potential energy indicate?

The particle will return to its original position.

The system is in stable equilibrium.

The system is in unstable equilibrium. (correct)

The potential energy is increasing.

Which condition is NOT true for a particle in stable equilibrium?

The potential energy is at maximum. Signup and view all the answers

What happens to the velocity after two colliding bodies move together?

They move with a common velocity. Signup and view all the answers

What is the S.I. unit of kinetic energy?

Joule (J) Signup and view all the answers

Which of the following statements is true regarding kinetic energy?

Kinetic energy is a scalar quantity. Signup and view all the answers

Which of the following is a condition for an elastic collision?

Total final momentum equals total initial momentum. Signup and view all the answers

When a bullet weighing 10 g is fired at 800 m/s and hits a mud wall, what is the bullet's final velocity?

100 m/s Signup and view all the answers

What is the dimensional formula for kinetic energy?

[ML^2T^-2] Signup and view all the answers

In the context of an elastic collision, what must remain constant regarding total energies?

Total final energy equals total initial energy. Signup and view all the answers

If the mass of a particle is represented by m and its velocity by v, which formula correctly represents kinetic energy?

K = 1/2 mv^2 Signup and view all the answers

What happens to body B1 when two bodies collide elastically and both have the same mass?

B1 comes to rest. Signup and view all the answers

What does the work done on a body by a net force equal?

The change in kinetic energy of the body Signup and view all the answers

If the mass of a block is divided in the ratio 2:3, what are the respective masses of the parts in terms of total mass m?

2m/5 and 3m/5 Signup and view all the answers

What is the equation that represents the relationship between final and initial kinetic energy?

K.E.(f) - K.E.(i) = W Signup and view all the answers

What is the formula used to calculate the work done based on kinetic energy and force?

W = K.E.(f) - K.E.(i) Signup and view all the answers

What is the velocity of the smaller part of the block after it breaks apart?

(8 i + 6 j) m/s Signup and view all the answers

What is the relationship between force and acceleration according to the given content?

F = m * a Signup and view all the answers

How is the change in kinetic energy represented mathematically?

K.E. = m * (v^2 - u^2) Signup and view all the answers

What is represented by K.E.(i) in the kinetic energy formula?

Initial kinetic energy Signup and view all the answers

What is the net acceleration calculated in the problem?

2.52 ms–2 Signup and view all the answers

What formula is used to calculate distance traveled in 10 seconds?

s = ut + at Signup and view all the answers

What is the total work done by the net force over the distance of 126 m?

635 J Signup and view all the answers

Which of the following statements about kinetic energy (K.E.) is correct?

K.E. cannot be lower than zero. Signup and view all the answers

What is the calculated final velocity at the end of 10 seconds?

25.2 m/s Signup and view all the answers

What does the potential energy (P.E.) relate to in regions where it exceeds total energy?

The particle cannot be present there. Signup and view all the answers

What is the work done by frictional force during the movement?

−247 J Signup and view all the answers

What is true about the change in kinetic energy according to the calculations?

It is equal to the work done by net force. Signup and view all the answers

What is the formula for calculating work done when a force is applied in a specific direction?

W = F ⋅ s cos q Signup and view all the answers

Under what condition is the work done considered zero when applying force?

When the displacement is zero. Signup and view all the answers

Which of the following units is used to measure work in the International System of Units (S.I.)?

Joule Signup and view all the answers

What is the relationship between force, velocity, and power?

P = Fv cos q Signup and view all the answers

When is work done considered positive?

When the angle between force and displacement is between 0 and π/2. Signup and view all the answers

What is the significance of the time factor in the definition of power?

It indicates how fast the work is done. Signup and view all the answers

What is the unit of power in the C.G.S system?

Erg/s Signup and view all the answers

Which statement is true regarding internal work?

It occurs when force is applied without displacement. Signup and view all the answers

Study Notes

Work and Energy

Work is defined as the product of force and displacement in the direction of the force.
Formula for work: W = F ⋅ s or W = F s cos θ.
Work is a scalar quantity.
Positive work occurs when the angle (θ) is between 0 and π/2; negative work when θ is between π/2 and 3π/2.
The SI unit of work is joule (J); CGS unit is erg (1 joule = 10^7 erg).
Internal work, where no useful energy is transferred (e.g., carrying a load while standing), results in zero work done.

Power

Power is the rate at which work is done over time.
Formula for power: P = W / t or P = F ⋅ v, where v is velocity and θ is the angle between force and velocity.
SI unit of power is watt (W), equivalent to 1 joule per second (1 W = 1 J/s).
Dimensions of power: [ML²T⁻³].
Power is also a scalar quantity.

Kinetic Energy

Kinetic energy (KE) is given by the formula KE = 1/2 mv², where m is mass and v is velocity.
SI unit of kinetic energy is joule (J) with dimensions [ML²T⁻²].
Kinetic energy is a scalar quantity.
The relationship between momentum (p) and kinetic energy: p = √(2mKE).

Collision Types

Elastic collision:
- Total momentum and total mechanical energy are conserved.
- Conditions for elastic collision include conservation of both momentum and energy.

Potential Energy

Potential energy can be defined in a conservative field where it depends on position.
Example of stable equilibrium: A marble in the bottom of a bowl, where potential energy is minimized.
Example of unstable equilibrium: A marble balanced on top of a bowl, where potential energy is maximized.

Work-Energy Theorem

The work-energy theorem states that the work done on an object by net force equals the change in its kinetic energy: W = KE(f) - KE(i).
Represents the relationship between work done and kinetic energy changes.

Additional Concepts

A block breaking into two parts affects the velocity of each part in proportion to their masses.
The relationship between work done, force, and displacement is integral to understanding energy transformations in mechanics.

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Description

Test your understanding of kinetic energy concepts with this quiz. It covers formulas related to the kinetic energy of particles and their relationships based on mass and velocity. Ideal for physics students aiming to strengthen their grasp of the topic.