At Earth's location, the intensity of sunlight is 1.5 kW / ${\mathbf{m}}^{\mathbf{2}}$ . If no energy escaped Earth, by how much would Earth's mass increase in 1 day?

How fast must an object be moving for its kinetic energy to equal its internal energy?

Classically, the net work done on an initially stationary object equals the final kinetic energy of the object. Verify that this also holds relativistically. Consider only one-dimension motion. It will be helpful to use the expression for p as a function of u in the following:

$W=\int Fdx=\int \frac{dp}{dt}dx=\int \frac{dx}{dt}dp=\int udp$

Particle $\mathbf{1}$, of mass role="math" localid="1657551290561" ${\mathit{m}}_{\mathbf{1}}$, moving at role="math" localid="1657551273841" $\mathbf{0}\mathbf{.}\mathbf{8}\mathbf{}\mathit{c}$ relative to the lab, collides head-on with particle $\mathbf{2}$ , of mass ${\mathit{m}}_{\mathbf{2}}$, moving at $\mathbf{0}\mathbf{.}\mathbf{6}\mathbf{}\mathit{c}$ relative to the lab. Afterward, there is a single stationary object. Find in terms of role="math" localid="1657551379188" ${\mathit{m}}_{\mathbf{1}}$

(a) ${\mathit{m}}_{\mathbf{2}}$

(b) the mass of the final stationary object; and

(c) the change in kinetic energy in this collision.

Using equations (2-20), show that

${{\mathit{y}}^{\mathbf{\text{'}}}}_{\mathbf{u}}\mathbf{=}\left(1-\frac{u_{x}v}{c^2}\right){\mathit{y}}_{\mathbf{v}}\mathbf{,}{\mathit{y}}_{\mathbf{u}}$

In a television picture tube, a beam of electrons is sent from the back to the front (screen) by an electron gun. When an electron strikes the screen, il causes a phosphor to glow briefly. To produce an image across the entire screen. the beam is electrically deflected up and down and left and right. The beam may sweep from left to right at a speed greater than c. Why is this not a violation of the claim that no information may travel faster than the speed of light?