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Physics with Calculus: Work, Energy, Momentum, and Collisions

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Terms in this set (20)

  • What is the work-energy theorem?

    The work-energy theorem states that the net work done on an object equals its change in kinetic energy.

  • Define kinetic energy.

    Kinetic energy is the energy an object has due to its motion, given by \(K=\frac{1}{2}mv^2\).

  • What is potential energy in a gravitational field?

    Gravitational potential energy is energy stored due to an object's position, calculated as \(U=mgh\).

  • What does an energy diagram represent?

    An energy diagram shows how potential and kinetic energy vary with position, illustrating energy conservation and transitions.

  • State the principle of conservation of mechanical energy.

    In the absence of non-conservative forces, the total mechanical energy (kinetic + potential) remains constant.

  • How is power defined in physics?

    Power is the rate at which work is done or energy is transferred, given by \(P=\frac{W}{t}\).

  • What is linear momentum?

    Linear momentum is the product of an object's mass and velocity, \(\vec{p}=m\vec{v}\).

  • Define impulse and its relation to momentum.

    Impulse is the change in momentum caused by a force applied over time, \(\vec{J}=\vec{F}\Delta t=\Delta \vec{p}\).

  • How does force relate to momentum?

    Force is the time rate of change of momentum, \(\vec{F}=\frac{d\vec{p}}{dt}\).

  • State the law of conservation of momentum.

    The total momentum of a closed system remains constant if no external forces act on it.

  • What distinguishes elastic and inelastic collisions?

    In elastic collisions, kinetic energy is conserved; in inelastic collisions, some kinetic energy is lost.

  • How is momentum conserved in collisions?

    During collisions, the vector sum of momenta before impact equals the vector sum after, \(\sum \vec{p}_{initial} = \sum \vec{p}_{final}\).

  • What is the formula for work done by a constant force?

    Work done is \(W=\vec{F} \cdot \vec{d} = Fd\cos\theta\), where θ is the angle between force and displacement.

  • Explain mechanical energy in a system.

    Mechanical energy is the sum of kinetic and potential energies in a system.

  • What is the significance of impulse in collisions?

    Impulse quantifies the effect of a force acting over a time interval, changing an object's momentum.

  • How do energy diagrams help analyze motion?

    They visualize how potential and kinetic energy interchange, helping predict speeds and positions.

  • What is the relationship between power and force?

    Power can be expressed as \(P=\vec{F} \cdot \vec{v}\), the dot product of force and velocity.

  • Describe an inelastic collision outcome.

    Objects stick together or deform, kinetic energy decreases, but momentum is conserved.

  • What is impulse-momentum theorem?

    The impulse applied to an object equals its change in momentum, \(\vec{J}=\Delta \vec{p}\).

  • How is kinetic energy related to velocity?

    Kinetic energy depends on the square of velocity, \(K=\frac{1}{2}mv^2\).