Podcast
Questions and Answers
What is true about stable equilibrium?
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?
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?
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?
Which condition is NOT true for a particle in stable equilibrium?
What happens to the velocity after two colliding bodies move together?
What happens to the velocity after two colliding bodies move together?
What is the S.I. unit of kinetic energy?
What is the S.I. unit of kinetic energy?
Which of the following statements is true regarding kinetic energy?
Which of the following statements is true regarding kinetic energy?
Which of the following is a condition for an elastic collision?
Which of the following is a condition for an elastic collision?
When a bullet weighing 10 g is fired at 800 m/s and hits a mud wall, what is the bullet's final velocity?
When a bullet weighing 10 g is fired at 800 m/s and hits a mud wall, what is the bullet's final velocity?
What is the dimensional formula for kinetic energy?
What is the dimensional formula for kinetic energy?
In the context of an elastic collision, what must remain constant regarding total energies?
In the context of an elastic collision, what must remain constant regarding total energies?
If the mass of a particle is represented by m and its velocity by v, which formula correctly represents kinetic energy?
If the mass of a particle is represented by m and its velocity by v, which formula correctly represents kinetic energy?
What happens to body B1 when two bodies collide elastically and both have the same mass?
What happens to body B1 when two bodies collide elastically and both have the same mass?
What does the work done on a body by a net force equal?
What does the work done on a body by a net force equal?
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?
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?
What is the equation that represents the relationship between final and initial kinetic energy?
What is the equation that represents the relationship between final and initial kinetic energy?
What is the formula used to calculate the work done based on kinetic energy and force?
What is the formula used to calculate the work done based on kinetic energy and force?
What is the velocity of the smaller part of the block after it breaks apart?
What is the velocity of the smaller part of the block after it breaks apart?
What is the relationship between force and acceleration according to the given content?
What is the relationship between force and acceleration according to the given content?
How is the change in kinetic energy represented mathematically?
How is the change in kinetic energy represented mathematically?
What is represented by K.E.(i) in the kinetic energy formula?
What is represented by K.E.(i) in the kinetic energy formula?
What is the net acceleration calculated in the problem?
What is the net acceleration calculated in the problem?
What formula is used to calculate distance traveled in 10 seconds?
What formula is used to calculate distance traveled in 10 seconds?
What is the total work done by the net force over the distance of 126 m?
What is the total work done by the net force over the distance of 126 m?
Which of the following statements about kinetic energy (K.E.) is correct?
Which of the following statements about kinetic energy (K.E.) is correct?
What is the calculated final velocity at the end of 10 seconds?
What is the calculated final velocity at the end of 10 seconds?
What does the potential energy (P.E.) relate to in regions where it exceeds total energy?
What does the potential energy (P.E.) relate to in regions where it exceeds total energy?
What is the work done by frictional force during the movement?
What is the work done by frictional force during the movement?
What is true about the change in kinetic energy according to the calculations?
What is true about the change in kinetic energy according to the calculations?
What is the formula for calculating work done when a force is applied in a specific direction?
What is the formula for calculating work done when a force is applied in a specific direction?
Under what condition is the work done considered zero when applying force?
Under what condition is the work done considered zero when applying force?
Which of the following units is used to measure work in the International System of Units (S.I.)?
Which of the following units is used to measure work in the International System of Units (S.I.)?
What is the relationship between force, velocity, and power?
What is the relationship between force, velocity, and power?
When is work done considered positive?
When is work done considered positive?
What is the significance of the time factor in the definition of power?
What is the significance of the time factor in the definition of power?
What is the unit of power in the C.G.S system?
What is the unit of power in the C.G.S system?
Which statement is true regarding internal work?
Which statement is true regarding internal work?
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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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