Question 1

A mass $$m is $$undergoing simple harmonic motion with amplitude $$A. $$When the mass is at a displacement $$x = \frac{A}{2}$$, what fraction of the total mechanical energy is kinetic energy?

Accepted Answer

$$\frac{3}{4}$$

Question 2

A block of mass $$0.20\ \mathrm{kg}$$ oscillates on a spring with a spring constant $$k = 40.0\ \mathrm{N/m}. $$What is the angular frequency $$\omega of $$the oscillation?

Accepted Answer

$$15.8\ \mathrm{rad/s}$$

Question 3

Which of the following is NOT true concerning Kepler's Laws or Newton's Law of Gravitation?

Accepted Answer

The gravitational force is always directed outward from the center of mass.

Question 4

An object is dropped from rest at an altitude of $$2R_E ($$where $$R_E is $$the radius of the Earth). Neglecting air resistance, what is its speed just before it hits the Earth's surface?

Accepted Answer

$$7.9\ \mathrm{km/s}$$

Question 5

A satellite orbits the Earth at a height equal to the Earth's radius above the surface. What is the orbital speed of the satellite?

Accepted Answer

$$\sqrt{\frac{GM_E}{2R_E}}$$

Question 6

A uniform hoop of mass $$M$$ and radius $$R is $$free to rotate about a horizontal axis passing through its edge. What is the period of small oscillations?

Accepted Answer

$$2\pi\sqrt{\frac{2R}{3g}}$$

Question 7

Two identical stars with mass $$M$$ orbit around their common center of mass, each at a radius $$R. $$What is the gravitational force on one star due to the other?

Accepted Answer

$$\frac{GM^2$}{4R^2$}$$

Question 8

A $$0.20\ \mathrm{kg}$$ block oscillates on a spring with amplitude $$0.020\ \mathrm{m}$$ and $$k = 40.0\ \mathrm{N/m}. $$What is the maximum kinetic energy of the block?

Accepted Answer

$$1.21\ \mathrm{J}$$

Question 9

A mass $$m$$ attached to a spring oscillates with position $$x(t) = A \cos(\omega t). At $$what time $$t$$ after $$t=0$$ does the block first reach half its amplitude?

Accepted Answer

$$t = \frac{\cos$$^{-1}$$(0.5)}{\omega}$$

Question 10

A block oscillates on a spring with $$x(t) = 0.020 \cos(157\ t)$$, where $$x is in $$meters and $$t in $$seconds. What is the period of oscillation?

Accepted Answer

$$T = \frac{2\pi}{157}\ \mathrm{s}$$

Question 11

A planet orbits a star in an elliptical orbit. At which point is its speed greatest?

Accepted Answer

At perihelion

Question 12

The escape speed from the surface of a planet of mass $$M$$ and radius $$R is $$given by:

Accepted Answer

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

Question 13

A block oscillates on a spring with amplitude $$A$$ and angular frequency $$\omega. At $$what displacement is the kinetic energy equal to the potential energy?

Accepted Answer

$$x = \frac{A}{\sqrt{2}}$$

Question 14

The total mechanical energy of a mass-spring system in simple harmonic motion is:

Accepted Answer

$$E = \frac{1}{2}kA^2$

Question 15

Two stars of mass $$M$$ each orbit each other at a distance $$2R$$ apart. What is the minimum energy required to separate them to infinity?

Accepted Answer

$$\frac{GM^2$}{4R}$$

Question 16

A block oscillates on a spring with $$k = 40.0\ \mathrm{N/m}$$ and amplitude $$0.020\ \mathrm{m}. $$What is the maximum speed of the block?

Accepted Answer

$$0.40\ \mathrm{m/s}$$

Study Notes: Oscillations, Gravitation, and Rotational Motion

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