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Questions and Answers
What is the result of the scalar product of two vectors A and B?
What is the result of the scalar product of two vectors A and B?
The scalar product of two vectors has a direction.
The scalar product of two vectors has a direction.
False
What is the formula for the scalar product of two vectors A and B if θ is the angle between them?
What is the formula for the scalar product of two vectors A and B if θ is the angle between them?
A.B = |A| |B| cos θ
The dot product of vectors A and B can be computed using the formula A.B = A B cos ______.
The dot product of vectors A and B can be computed using the formula A.B = A B cos ______.
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Match the following terms with their correct definitions:
Match the following terms with their correct definitions:
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What does the work done by the spring force depend on?
What does the work done by the spring force depend on?
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The work done by the spring force is always positive.
The work done by the spring force is always positive.
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What is the mathematical expression for the work done by the spring force when it is compressed to displacement $x_c < 0$?
What is the mathematical expression for the work done by the spring force when it is compressed to displacement $x_c < 0$?
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What is the work done by a force when there is no displacement?
What is the work done by a force when there is no displacement?
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The work done by the spring force is represented by the area of the _____ in the force vs. displacement graph.
The work done by the spring force is represented by the area of the _____ in the force vs. displacement graph.
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Match the following variables with their descriptions:
Match the following variables with their descriptions:
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An object can do work without any motion occurring.
An object can do work without any motion occurring.
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What equation represents the work done by a force in the direction of displacement?
What equation represents the work done by a force in the direction of displacement?
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If the force applied is zero, then the work done is ___.
If the force applied is zero, then the work done is ___.
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Match the following scenarios with their corresponding outcomes:
Match the following scenarios with their corresponding outcomes:
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What does Hooke’s law state about the spring force?
What does Hooke’s law state about the spring force?
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The work done by a spring force in a cyclic process is non-zero.
The work done by a spring force in a cyclic process is non-zero.
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What is the formula for potential energy (V) of a spring?
What is the formula for potential energy (V) of a spring?
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At maximum compression, the kinetic energy of the car is converted entirely into the potential energy of the ______.
At maximum compression, the kinetic energy of the car is converted entirely into the potential energy of the ______.
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Match the terms with their definitions:
Match the terms with their definitions:
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Study Notes
Work, Energy, and Power
- The terms work, energy, and power have precise meanings in physics, differing from everyday usage.
- Work is the product of the component of force in the direction of displacement and the displacement magnitude.
- Work is a scalar quantity and work done can be positive or negative.
- Work done is zero if displacement is zero, force is zero, or if the force and displacement are perpendicular.
- Kinetic energy (KE) is the energy of motion, given by KE = 1/2 * mv² where m = mass and v = velocity.
- The work-energy theorem states that the change in a particle's kinetic energy is equal to the net work done on it.
- Potential energy (PE) is the stored energy of a system due to its position or configuration.
- Gravitational potential energy is PE = mgh, where m = mass, g = acceleration due to gravity, and h = height.
- Potential energy of a spring is PE = 1/2kx², where k = spring constant and x = displacement from equilibrium.
- Mechanical energy is the sum of kinetic and potential energies.
- Power is the rate at which work is done or energy is transferred, given by Power = work/time.
- Instantaneous power is the limiting value of average power as the time interval approaches zero, calculated as P = dW/dt = F.v (where v is velocity).
Scalar Product
- A scalar product of two vectors A and B is a scalar quantity given by: A • B = AB cos θ, where θ is the angle between A and B.
- Geometrically, the scalar product is the product of the magnitude of one vector and the component of the other along the first.
- Scalar product obeys the commutative and distributive laws.
Collisions
- In collisions, the total linear momentum (m•v) is conserved (quantity that does not change).
- Elastic collision involves no loss of kinetic energy, whereas in inelastic collisions, kinetic energy changes, and some energy may be converted to other forms (e.g., heat).
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Description
Test your understanding of the concepts of work, energy, and power in physics. This quiz covers definitions, formulas, and applications of kinetic and potential energy, as well as the work-energy theorem. Perfect for students looking to solidify their knowledge in these fundamental physics topics.
