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Physics with Calculus - Core Concepts and Problem Solving

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Termini in questo insieme (27)

  • What is the first step in Jonathan's Physics Problem-Solving Chain?

    Read the problem carefully without using a calculator to understand the physical story.

  • How do you add vectors in two dimensions?

    Add the x and y components separately, then find the resultant magnitude with \(R=\sqrt{R_x^2 + R_y^2}\).

  • What does the slope of an x vs t graph represent?

    The slope of an x-t graph represents velocity.

  • What is the meaning of constant acceleration in terms of velocity and displacement graphs?

    Velocity increases linearly with time; displacement graph is curved upward; acceleration is constant.

  • How is projectile motion analyzed in two dimensions?

    Separate motion into independent horizontal (constant velocity) and vertical (constant acceleration) components sharing the same time.

  • What is a free-body diagram (FBD)?

    A diagram showing all external forces acting on a chosen object or system, isolating it from surroundings.

  • Why do Newton's third-law forces not cancel on a single-object FBD?

    Because they act on different objects, not the same object.

  • How do you resolve weight components on an inclined plane?

    Parallel component: \(mg \sin \theta\); perpendicular component: \(mg \cos \theta\).

  • What is the formula for centripetal acceleration and force?

    \(a_c=\frac{v^2}{r}\) and \(F_{in}=m\frac{v^2}{r}\).

  • State Newton's universal law of gravitation.

    \(F=G\frac{m_1 m_2}{r^2}\), where G is gravitational constant and r is center-to-center distance.

  • What is the work done by a constant force?

    \(W=F d \cos \theta\), where θ is angle between force and displacement.

  • Write the kinetic energy formula.

    \(K=\frac{1}{2}mv^2\), energy due to translational motion.

  • What is the work-energy theorem?

    Net work done on an object equals its change in kinetic energy: \(W_{net}=\Delta K\).

  • Define linear momentum and impulse.

    Momentum: \(p=mv\). Impulse: \(J=F_{avg} \Delta t=\Delta p\).

  • What is conserved in an isolated collision system?

    Total linear momentum is conserved: \(\sum p_{before} = \sum p_{after}\).

  • What are the rotational analogs of position, velocity, and acceleration?

    Angular displacement θ, angular velocity ω, and angular acceleration α.

  • How do you convert rpm to angular velocity in rad/s?

    \(\omega=2\pi \frac{rpm}{60}\).

  • What is torque and how is it calculated?

    \(\tau = r F \sin \phi\), where r is lever arm and φ is angle between force and lever arm.

  • State Hooke's law for spring force.

    \(F_s = -kx\), restoring force proportional and opposite to displacement.

  • What is the period of a mass-spring system in simple harmonic motion?

    \(T=2\pi \sqrt{\frac{m}{k}}\).

  • What is the wave speed formula?

    \(v=f \lambda\), wave speed equals frequency times wavelength.

  • State Bernoulli's equation for ideal fluid flow.

    \(P + \frac{1}{2} \rho v^2 + \rho g y = \text{constant}\) along a streamline.

  • What is Archimedes' principle for buoyant force?

    \(F_b = \rho_{fluid} g V_{displaced}\).

  • Write the ideal gas law.

    \(PV = nRT\), relating pressure, volume, moles, gas constant, and temperature.

  • What is the first law of thermodynamics energy balance?

    \(\Delta U = Q - W\), change in internal energy equals heat added minus work done by system.

  • Define heat engine efficiency.

    \(\eta = \frac{W}{Q_h} = 1 - \frac{Q_c}{Q_h}\), work output divided by heat input.

  • What is entropy change for reversible heat transfer?

    \(\Delta S = \frac{Q_{rev}}{T}\), where T is absolute temperature.