In an Earth reference frame, a star is 82 light-years away. How fast would you have to travel so that to you the distance would be only 35 light-years?

You travel to a star $135$ light-years from Earth at a speed of $2.90 \times 10^8 \mathrm{~m} / \mathrm{s}$. What do you measure this distance to be?

A certain type of elementary particle travels at a speed of $2.70 \times 10^{8} \mathrm{m} / \mathrm{s} .$ At this speed, the average lifetime is measured to be $4.76 \times 10^{-6} \mathrm{s}$. What is the particle's lifetime at rest?

$2.44 \mathrm{~m}$ long coil containing $265$ loops is wound on an iron core (average $\mu=1850 \mu_0$ ) along with a second coil of $115$ loops. The loops of each coil have a radius of $2.00 \mathrm{~cm}$. Determine the mutual inductance $M$.

A 2.44-m-long coil containing 225 loops is wound on an iron core (average $\mu=1850 \mu_0$ ) along with a second coil of 115 loops. The loops of each coil have a radius of $2.00 \mathrm{~cm}$. If the current in the first coil drops uniformly from $12.0 \mathrm{~A}$ to zero in $98.0 \mathrm{~ms}$, determine: $(a)$ the mutual inductance $M.

A spaceship passes you at a speed of 0.750c. You measure its length to be 28.2 m. How long would it be when at rest?

A Carnot engine's operating temperatures are $210^{\circ} \mathrm{C}$ and $45^{\circ} \mathrm{C}$. The engine's power output is 950 W. Calculate the rate of heat output.

A Carnot engine's operating temperatures are $210^{\circ} \mathrm{C}$ and $45^{\circ} \mathrm{C}$. The engine's power output is $960 \mathrm{~W}$. Calculate the rate of heat output.

Light strikes perpendicular to a thin film in air. Considering the wavelength of light inside the film, then if the film has a thickness that is $(a)$ $\frac{1}{4}$ of a wavelength, constructive interference will always occur. $(b)$ $\frac{1}{4}$ of a wavelength, destructive interference will always occur. $(c)$ $\frac{1}{2}$ of a wavelength, constructive interference will always occur. $(d)$ $\frac{1}{2}$ of a wavelength, destructive interference will always occur. $(e)$ None of the above is always true.

How much energy would be required to break a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy difference is called the total binding energy of the $\frac{4}{2}$He nucleus.)

An unknown particle is measured to have a negative charge and a speed of $2.24 \times 10^{8} \mathrm{m} / \mathrm{s}$. Its momentum is determined to be $3.07 \times 10^{-22} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$. Identify the particle by finding its rest mass.

The Sun radiates energy at a rate of about $4 \times 10^{26} \mathrm{W}$. Estimate how long the Sun could last if it radiated constantly at this rate.

The critical angle for total internal reflection at a boundary between two materials is $52\degree$. What is Brewster's angle at this boundary?

The Sun radiates energy at a rate of about $4 \times 10^{26} \mathrm{W}$. How long does it take for the Sun to lose a mass equal to that of Earth?