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How is the scalar product of two vectors, A and B, denoted?
How is the scalar product of two vectors, A and B, denoted?
A·B
What is the formula for calculating the scalar product of two vectors, A and B?
What is the formula for calculating the scalar product of two vectors, A and B?
AB = A·B cos θ
The scalar product of two vectors is always a scalar quantity.
The scalar product of two vectors is always a scalar quantity.
True
The scalar product of two vectors is commutative, meaning the order of multiplication does not affect the result.
The scalar product of two vectors is commutative, meaning the order of multiplication does not affect the result.
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The scalar product of two vectors follows the distributive law.
The scalar product of two vectors follows the distributive law.
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What is the formula for the dot product of the unit vectors i, j, and k?
What is the formula for the dot product of the unit vectors i, j, and k?
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What is the formula for calculating the scalar product of two vectors, A and B, in terms of their components?
What is the formula for calculating the scalar product of two vectors, A and B, in terms of their components?
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What is the value of the dot product of two vectors, A and B, when they are perpendicular to each other?
What is the value of the dot product of two vectors, A and B, when they are perpendicular to each other?
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What is the relationship between the magnitude of a vector and its dot product with itself?
What is the relationship between the magnitude of a vector and its dot product with itself?
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What is the formula for calculating the work done by a force, F, over a displacement, d?
What is the formula for calculating the work done by a force, F, over a displacement, d?
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Work is done even if the force acting on an object has zero magnitude.
Work is done even if the force acting on an object has zero magnitude.
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Work is done even if the displacement of the object is zero.
Work is done even if the displacement of the object is zero.
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Work can be positive, negative, or zero.
Work can be positive, negative, or zero.
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What is the formula for calculating kinetic energy, K?
What is the formula for calculating kinetic energy, K?
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Kinetic energy is a scalar quantity.
Kinetic energy is a scalar quantity.
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What is the relationship between the work done on an object and its change in kinetic energy?
What is the relationship between the work done on an object and its change in kinetic energy?
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The work-energy theorem applies only to constant forces.
The work-energy theorem applies only to constant forces.
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What is the formula for calculating the power, P, of a force?
What is the formula for calculating the power, P, of a force?
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Power is a scalar quantity.
Power is a scalar quantity.
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What is the SI unit of power?
What is the SI unit of power?
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The total mechanical energy of a system is conserved when only conservative forces are acting on it.
The total mechanical energy of a system is conserved when only conservative forces are acting on it.
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Frictional force is a conservative force.
Frictional force is a conservative force.
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What is the formula for calculating the potential energy, V(x), of a spring with a spring constant, k, and displacement, x?
What is the formula for calculating the potential energy, V(x), of a spring with a spring constant, k, and displacement, x?
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The total mechanical energy of a system is always conserved, regardless of internal and external forces.
The total mechanical energy of a system is always conserved, regardless of internal and external forces.
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In an elastic collision, both kinetic energy and momentum are conserved.
In an elastic collision, both kinetic energy and momentum are conserved.
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In an inelastic collision, both kinetic energy and momentum are conserved.
In an inelastic collision, both kinetic energy and momentum are conserved.
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The potential energy of a system is always zero at its equilibrium position.
The potential energy of a system is always zero at its equilibrium position.
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In a collision, the total linear momentum is conserved at every instant of the collision.
In a collision, the total linear momentum is conserved at every instant of the collision.
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Study Notes
Work, Energy, and Power
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Work: Defined as the product of force's component in the displacement direction and displacement magnitude.
- Mathematically: W = Fd cos θ, where F is force, d is displacement, and θ is the angle between them.
- Unit: Joule (J)
- Zero work when displacement is zero, force is zero, or force and displacement are perpendicular.
- Positive/negative work depending on the angle between force and displacement.
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Kinetic energy (KE): Energy of motion.
- Formula: KE = 1/2 mv², where m is mass and v is velocity.
- Unit: Joule (J)
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Work-Energy Theorem: Change in kinetic energy equals the net work done.
- Formula: ΔKE = Wnet
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Potential Energy (PE): Energy due to position or configuration.
- Gravitational PE (near Earth's surface) : PE = mgh, where m is mass, g is gravity and h is height.
- Spring PE: PE = ½kx², where k is the spring constant and x is the displacement from equilibrium.
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Conservation of Mechanical Energy: Sum of kinetic and potential energy remains constant if only conservative forces act.
- Formula: KEi + PEi = KEf + PEf
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Power: Rate of doing work or transferring energy.
- Formula: P = W/t (average power) , P = dW/dt (instantaneous power)
- P = Fv (where F is force in direction of velocity).
- Unit: Watt (W)
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Collisions: Momentum is conserved in all collisions
- Elastic Collisions: Kinetic energy is conserved.
- Inelastic Collisions: Kinetic energy is not conserved.
Scalar Product
- Scalar product of vectors A and B (dot product): A ⋅ B = AB cos θ, Where A and B are the magnitudes of the vectors, and θ is the angle between them
- A ⋅ B = (AxBx) + (AyBy) + (AzBz).
Work Done by a Variable Force
- The work done by a variable force is equal to the area under the force-displacement curve.
- Formula: W = ∫xixf F(x) dx
Types of Collisions
- Completely Inelastic Collisions: The colliding objects stick together after collision
Collisions in One Dimension
- Momentum Conservation in one dimension: m₁v₁ᵢ = m₁v₁f + m₂v₂f (where m and v are mass and velocity respectively, subscripts i and f indicate initial and final)
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Kinetic Energy Conservation in one dimension:
- For elastic collisions: (1/2)m₁v₁ᵢ² = (1/2)m₁v₁f² + (1/2)m₂v₂f²
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