Question 1

Three identical bodies of mass $$m$$ are placed at the corners of a right triangle with legs of length $$a. $$What is the magnitude of the net gravitational force on the body at the right angle vertex?

Accepted Answer

$$\sqrt{2}Gm^2$/a^2$

Question 2

A rock is thrown vertically upward from the Earth's surface with an initial speed equal to half the escape velocity. Neglecting air resistance, what is the maximum altitude (measured from the ground) the rock will reach, in terms of Earth's radius $$R$$?

Accepted Answer

$$R/3$$

Question 3

A body undergoes simple harmonic motion. At which point in its velocity vs. time graph is the body at the center of oscillation and moving in the positive direction?

Accepted Answer

1 only

Question 4

A researcher models the tip of a cilium as a simple harmonic oscillator. At $$t=0$$, the tip is at equilibrium. Four seconds later, it is at its maximum displacement $$d. $$Which equation best describes the position $$x(t) of $$the tip as a function of time?

Accepted Answer

$$x(t) = d \sin\left(\frac{\pi}{8} t\right)$$

Question 5

For the cilium modeled as a simple harmonic oscillator, at which position is the magnitude of the force on the tip greatest?

Accepted Answer

Both $$x = d$$ and $$x = -d$$

Question 6

A satellite is in a circular orbit of radius $$2R$$ around a planet of mass $$M. $$What is the gravitational force acting on the satellite of mass $$m$$?

Accepted Answer

$$G M m / (2R)^2$

Question 7

A mass on a spring oscillates with amplitude $$A$$ and period $$T. $$How much time does it take to move from equilibrium to maximum displacement?

Accepted Answer

$$T/4$$

Question 8

If the escape velocity from a planet is $$v_{esc}$$, what is the minimum kinetic energy required for a mass $$m to $$escape the planet's gravity from its surface?

Accepted Answer

$$\frac{1}{2} m v_{esc}^2$$

Question 9

A pendulum in a grandfather clock swings with a period of $$2$$ seconds. If the length of the pendulum is doubled, what will be the new period?

Accepted Answer

$$2\sqrt{2}$$ seconds

Question 10

A mass $$m is $$attached to a spring with spring constant $$k$$ and oscillates with amplitude $$A. $$What is the maximum acceleration experienced by the mass?

Accepted Answer

$$\frac{kA}{m}$$

Question 11

A medical device uses a tiny oscillating mass to measure vibrations in the human body. If the device is calibrated so that the mass completes one oscillation in $$0.5$$ seconds, what is its angular frequency $$\omega$$?

Accepted Answer

$$4\pi$$ rad/s

Question 12

A block is attached to a horizontal spring and oscillates with simple harmonic motion. At what position is the kinetic energy of the block maximum?

Accepted Answer

At equilibrium position

Question 13

A comet approaches the Sun from far away with negligible initial speed. What is its speed when it is at a distance $$R$$ from the Sun (mass $$M$$)?

Accepted Answer

$$\sqrt{2GM/R}$$

Question 14

A mass $$m is $$oscillating on a spring with amplitude $$A$$ and period $$T. $$What is the total mechanical energy of the system?

Accepted Answer

$$\frac{1}{2} k A^2$

Question 15

A patient’s cilia are modeled as simple harmonic oscillators with period $$T = 16 s. $$How long does it take for the cilium tip to move from equilibrium to maximum displacement?

Accepted Answer

$$4 s$$

Question 16

A mass $$m is $$placed at a distance $$a$$ from two other identical masses, each also of mass $$m$$, located at perpendicular axes. What is the direction of the net gravitational force on the mass at the origin?

Accepted Answer

Along the diagonal between the two other masses

Question 17

A mass is oscillating with simple harmonic motion. At which point is the restoring force zero?

Accepted Answer

At equilibrium position

Question 18

A rock is thrown upward from the Earth's surface with a speed less than escape velocity. Which of the following best describes its motion?

Accepted Answer

It will rise to a maximum height and then fall back to Earth

Question 19

A mass $$m$$ attached to a spring oscillates with period $$T. If $$the mass is quadrupled, what happens to the period?

Accepted Answer

It doubles

Question 20

A cilium tip modeled as a simple harmonic oscillator has maximum force at which points?

Accepted Answer

At maximum displacement in either direction

Discussion 11

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