91Ó°ÊÓ

Within cells, small organelles containing newly synthesized proteins are transported along microtubules by tiny molecular motors called kinesins. What force does a kinesin molecule need to deliver in order to accelerate an organelle with mass \(0.01 \mathrm{pg}\left(10^{-17} \mathrm{kg}\right)\) from 0 to \(1 \mu \mathrm{m} / \mathrm{s}\) within a time of \(10 \mu \mathrm{s} ?\)

A flat, circular metal disk of uniform thickness has a radius of $3.0 \mathrm{cm} .\( A hole is drilled in the disk that is \)1.5 \mathrm{cm}$ in radius. The hole is tangent to one side of the disk. Where is the \(\mathrm{cm}\) of the disk now that the hole has been drilled? [Hint: The original disk (before the hole is drilled) can be thought of as having two pieces-the disk with the hole plus the smaller disk of metal drilled out. Write an equation that expresses \(x_{\mathrm{CM}}\) of the original disk in terms of the \(x_{\mathrm{CM}}\) 's of the two pieces. since the thickness is uniform, the mass of any piece is proportional to its area.]

Two pendulum bobs have equal masses and lengths \((5.1 \mathrm{m}) .\) Bob \(\mathrm{A}\) is initially held horizontally while bob \(\mathrm{B}\) hangs vertically at rest. Bob A is released and collides elastically with bob B. How fast is bob B moving immediately after the collision?

Two identical gliders, each with elastic bumpers and mass \(0.10 \mathrm{kg},\) are on a horizontal air track. Friction is negligible. Glider 2 is stationary. Glider 1 moves toward glider 2 from the left with a speed of $0.20 \mathrm{m} / \mathrm{s} .$ They collide. After the collision, what are the velocities of glider 1 and glider \(2 ?\)

A radium nucleus (mass 226 u) at rest decays into a radon nucleus (symbol Rn, mass 222 u) and an alpha particle (symbol \(\alpha,\) mass 4 u). (a) Find the ratio of the speeds \(v_{\alpha} / v_{\mathrm{Rn}}\) after the decay. (b) Find the ratio of the magnitudes of the momenta \(p_{\alpha} / p_{\mathrm{Rn}^{*}}\) (c) Find the ratio of the kinetic energies \(K_{\alpha} / K_{\mathrm{Rn}} .\) (Note: "u" is a unit of mass; it is not necessary to convert it to kg.)