Physics Problems: Pendulums, Motion, and Forces

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Questions and Answers

A simple pendulum of length $l$ with a bob of mass $m$ is oscillating with a small amplitude. If the mass of the bob is doubled, what is the effect on the pendulum's period?

  • The period is multiplied by $\sqrt{2}$.
  • The period remains unchanged. (correct)
  • The period is halved.
  • The period is doubled.

A particle is moving under the influence of a central force. Which of the following quantities is conserved?

  • Angular momentum (correct)
  • Linear momentum
  • Potential energy
  • Kinetic energy

Two masses, $m_1$ and $m_2$, are connected by a massless string over a frictionless pulley. If $m_1 > m_2$, what is the acceleration of the mass $m_1$?

  • $\frac{m_1 - m_2}{m_1 + m_2}g$ (correct)
  • $\frac{m_1}{m_1 + m_2}g$
  • $g$
  • $\frac{m_2}{m_1 + m_2}g$

A projectile is launched at an angle $\theta$ with respect to the horizontal with an initial velocity $v_0$. Assuming negligible air resistance, what angle $\theta$ maximizes the range of the projectile?

<p>45 degrees (A)</p> Signup and view all the answers

A block of mass $m$ is sliding down an inclined plane with a coefficient of kinetic friction $\mu_k$. The angle of the incline with the horizontal is $\theta$. What is the acceleration of the block?

<p>$g(\sin\theta - \mu_k \cos\theta)$ (A)</p> Signup and view all the answers

A particle of mass $m$ is moving in a circular path of radius $r$ with constant speed $v$. What is the magnitude of the angular momentum of the particle about the center of the circle?

<p>$mvr$ (C)</p> Signup and view all the answers

A spring with spring constant $k$ is stretched a distance $x$ from its equilibrium position. What is the potential energy stored in the spring?

<p>$\frac{1}{2}kx^2$ (B)</p> Signup and view all the answers

Two objects collide inelastically. Which of the following is always conserved?

<p>Momentum (C)</p> Signup and view all the answers

A rigid body is rotating about a fixed axis. Which of the following quantities is the same for all points in the body?

<p>Angular velocity (C)</p> Signup and view all the answers

What is the number of degrees of freedom for a diatomic molecule, considering it can both rotate and vibrate?

<p>6 (D)</p> Signup and view all the answers

Flashcards

Classical Mechanics

Study of motion and forces, uses Newton's Laws.

Inertial Frame

Inertial reference frames move at constant velocity.

Inertia

Property resisting changes in motion; proportional to mass.

Newton's Second Law

F = ma; force equals mass times acceleration.

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Newton's Third Law

Every action has an equal and opposite reaction.

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Inertial Mass

Measure of how force changes an object's motion.

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Friction

A force exerted by a surface that opposes motion.

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Kinetic Friction

Friction force proportional to the normal force ($F_f = \mu F_N$).

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Static Friction

Maximum friction before movement starts ($F_s \le \mu_s F_N$).

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