Podcast
Questions and Answers
What is the formula for calculating work when the force is constant?
What is the formula for calculating work when the force is constant?
- W = F × d
- W = ∫ F dx
- W = F . ds (correct)
- W = F / ds
The change in kinetic energy is equivalent to what?
The change in kinetic energy is equivalent to what?
- Potential energy
- Work done (correct)
- Impulse
- Moment of inertia
What is the expression for impulse when force is variable?
What is the expression for impulse when force is variable?
- I = m v
- I = F × t
- I = ∫ m dv/dt dt
- I = ∫ F dt (correct)
What does the coefficient of restitution (Ge) indicate for a perfectly elastic body?
What does the coefficient of restitution (Ge) indicate for a perfectly elastic body?
In a collision of two spheres, which equation represents conservation of momentum?
In a collision of two spheres, which equation represents conservation of momentum?
What is the relationship between kinetic energy and work done when an object starts from rest?
What is the relationship between kinetic energy and work done when an object starts from rest?
What type of impact occurs when two objects collide at an angle?
What type of impact occurs when two objects collide at an angle?
What is the expression for the final velocity of mass C after the second collision with mass B?
What is the expression for the final velocity of mass C after the second collision with mass B?
Which equation describes the relationship between the initial and final velocities during the first collision between C and A?
Which equation describes the relationship between the initial and final velocities during the first collision between C and A?
What is the final velocity of mass A after the last collision with mass C?
What is the final velocity of mass A after the last collision with mass C?
In the scenario of oblique impact, what condition affects the vertical components of the velocities?
In the scenario of oblique impact, what condition affects the vertical components of the velocities?
After three collisions, how are the final velocities of A, B, and C related?
After three collisions, how are the final velocities of A, B, and C related?
In the collision between masses C and A, what is the outcome of the direction of mass C after the collisions?
In the collision between masses C and A, what is the outcome of the direction of mass C after the collisions?
What is the value of the final velocity of mass B after all the collisions have occurred?
What is the value of the final velocity of mass B after all the collisions have occurred?
What is the equation relating the masses and velocities during the oblique impact between two spheres?
What is the equation relating the masses and velocities during the oblique impact between two spheres?
Flashcards
Impulse
Impulse
The change in velocity of an object due to a collision with another object.
Coefficient of Restitution (e)
Coefficient of Restitution (e)
A measure of how much energy is lost during a collision.
Initial Velocity (u)
Initial Velocity (u)
The velocity of an object before a collision.
Final Velocity (v)
Final Velocity (v)
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Conservation of Linear Momentum
Conservation of Linear Momentum
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Direct Impact
Direct Impact
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Oblique Impact
Oblique Impact
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Angle of Impact (θ)
Angle of Impact (θ)
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Work done by a constant force
Work done by a constant force
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Work done by a variable force
Work done by a variable force
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Kinetic Energy
Kinetic Energy
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Potential Energy
Potential Energy
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Work-Energy Principle
Work-Energy Principle
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Conservation of Mechanical Energy
Conservation of Mechanical Energy
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Study Notes
Work and Energy
- Work (W): The product of force (F) and displacement (ds) in the direction of the force. W = F ⋅ ds. If the force is constant, W = Fd cosθ, where 'd' is the displacement magnitude and θ is the angle between the force and displacement vectors.
- Work-Energy Theorem: The net work done on an object is equal to the change in its kinetic energy (KE). W = ΔKE.
- Kinetic Energy (KE): The energy of motion, calculated as KE = 1/2mv².
- Potential Energy (PE): The energy stored in an object due to its position or configuration. PE = mgh, where 'm' is mass, 'g' is acceleration due to gravity, and 'h' is height.
- Conservation of Energy: Total energy (KE + PE) remains constant in a closed system. Therefore, ΔPE = -ΔKE.
- Principle of Work: The work done by a force on an object is equal to the change in the object's kinetic energy, plus any potential energy involved.
Collisions and Impulse
- Impulse (I): The product of force (F) and time (Δt) during which the force acts. I = FΔt. For constant force, I = F⋅Δt.
- Impulse-Momentum Theorem: The impulse acting on an object is equal to the change in its momentum. I = Δp.
- Momentum (p): The product of mass (m) and velocity (v). p = mv.
- Conservation of Momentum: Total momentum remains constant in a closed system. m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ (for two objects).
- Coefficient of Restitution (e): A measure of the elasticity of a collision. e = |(v₂ - v₁)/(u₁ - u₂)|, where (v₂ - v₁) is the relative velocity after collision, and (u₁ - u₂) is the relative velocity before collision.
- Direct Collision: Collisions happen along the line joining the centers of colliding objects.
- Oblique Collision: Collisions occurring at an angle to the line connecting the centers of the objects.
- Perfectly Elastic Collisions: Collisions where kinetic energy is conserved. e=1
- Inelastic Collisions: Collisions where some kinetic energy is lost. 0<e<1.
Additional Concepts
- Types of Impact:
- Direct
- Oblique
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