91Ó°ÊÓ

You are asked to design a spring that will give a 1160-kg satellite a speed of 2.50 m/s relative to an orbiting space shuttle. Your spring is to give the satellite a maximum acceleration of 5.00g. The spring’s mass, the recoil kinetic energy of the shuttle, and changes in gravitational potential energy will all be negligible. (a) What must the force constant of the spring be? (b) What distance must the spring be compressed?

After emergencies with major blood loss, a patient is placed in the Trendelen burg position, in which the foot of the bed is raised to get maximum blood flow to the brain. If the coefficient of static friction between atypical patient and the bed sheets is 1.20, what is the maximum angle at which the bed can be tilted with respect to the floor before the patient begins to slide?

A jet plane comes in for a downward dive as shown in Fig. E3.25. The bottom part of the path is a quarter circle with a radius of curvature of 280 m. According to medical tests, pilots will lose consciousness when they pull out of a dive at an upward acceleration greater than 5.5g. At what speed (in m/s and in mph) will the pilot black out during this dive?

Deimos, a moon of Mars, is about 12 km in diameter with mass $\mathbf{1}\mathbf{.}\mathbf{5}\mathit{x}{\mathbf{10}}^{\mathbf{15}\mathbf{}}\mathit{k}\mathit{g}$. Suppose you are stranded alone on Deimos and want to play a one-person game of baseball. You would be the pitcher, and you would be the batter! (a) With what speed would you have to throw a baseball so that it would go into a circular orbit just above the surface and return to you so you could hit it? Do you think you could actually throw it at this speed? (b) How long (in hours) after throwing the ball should you be ready to hit it? Would this be an action-packed baseball game?

A hunter on a frozen, essentially frictionless pond uses a rifle that shoots 4.20 g bullets at 965 m/s. The mass of the hunter (including his gun) is 72.5 kg, and the hunter holds tight to the gun after firing it. Find the recoil velocity of the hunter if he fires the rifle (a) horizontally and (b) at 56.0 degrees above the horizontal.

Centrifuge. An advertisement claims that a centrifuge takes up only 0.127 m of bench space but can produce a radial acceleration of 3000g at 5000 revs/min. Calculate the required radius of the centrifuge. Is the claim realistic?

A small block is attached to an ideal spring and is moving in SHM on a horizontal frictionless surface. The amplitude of the motion is 0.165 m. The maximum speed of the block is 3.90 m/s. What is the maximum magnitude of the acceleration of the block?

The surface pressure on Venus is 92 atm, and the acceleration due to gravity there is 0.894 g. In a future exploratory mission, an upright cylindrical tank of benzene is sealed at the top but still pressurized at 92 atm just above the benzene. The tank has a diameter of 1.72 m, and the benzene column is 11.50 m tall. Ignore any effects due to the very high temperature on Venus. (a) What total force is exerted on the inside surface of the bottom of the tank? (b) What force does the Venusian atmosphere exert on the outside surface of the bottom of the tank? (c) What total inward force does the atmosphere exert on the vertical walls of the tank?

Crates A and B sit at rest side by side on a frictionless horizontal surface. They have masses ${\mathbf{m}}_{\mathbf{A}}$and ${\mathbf{m}}_{\mathbf{B}}$respectively. When a horizontal forcerole="math" localid="1663766019250" $\stackrel{â‡\P Ä}{\mathbf{F}}$is applied to crate A, the two crates move off to the right. (a) Draw clearly labeled free-body diagrams for crate A and for crate B. Indicate which pairs of forces, if any, are third-law action-reaction pairs. (b) If the magnitude of $\stackrel{\mathbf{→}}{\mathbf{F}}$is less than the total weight of the two crates, will it cause the crates to move? Explain.

A jet plane at takeoff can produce sound of intensity \[10.0 {W \mathord{\left/

{\vphantom {W {{m^2}}}} \right.

\nulldelimiterspace} {{m^2}}}\]at \[30.0 m\]away. But you prefer the tranquil sound of normal conversation, which is\[1.0 {{\mu W} \mathord{\left/

{\vphantom {{\mu W} {{m^2}}}} \right.

\nulldelimiterspace} {{m^2}}}\]. Assume that the plane behaves like a point source of sound. (a) What is the closest distance you should live from the airport runway to preserve your peace of mind? (b) What intensity from the jet does your friend experience if she lives twice as far from the runway as you do? (c) What power of sound does the jet produce at takeoff?