91Ó°ÊÓ

A helicopter has a large main rotor that rotates in a horizontal plane and provides lift. There is also a small rotor on the tail that rotates in a vertical plane. What is the purpose of the tail rotor? (Hint: If there were no tail rotor, what would happen when the pilot changed the angular speed of the main rotor?) Some helicopters have no tail rotor, but instead, have two large main rotors that rotate in a horizontal plane. Why is it important that the two main rotors rotate in opposite directions?

Two objects of mass Mand 5Mare at rest on a horizontal,frictionless table with a compressed spring of negligible massbetween them. When the spring is released, which of the followingstatements are true?

(a) The two objects receive equal magnitudes of momentum.

(b) The two objects receive equal amountsof kinetic energy from the spring.

(c) The heavier object gainsmore kinetic energy than the lighter object.

(d) The lighter objectgains more kinetic energy than the heavier object.

Explain yourreasoning in each case.

If $\stackrel{→}{A}$.$\stackrel{→}{B}$=0 does it necessarily follow that A = 0 or B= 0? Explain. (b) If $\stackrel{→}{A}×\stackrel{→}{B}=0$$\stackrel{→}{A}$ = 0, does it necessarily follow that A = 0 or B = 0? Explain.

A ball is dropped from rest and feels air resistance as it falls. Which of the graphs in Fig. Q5.25 best represents its acceleration as a function of time?

When rubber mounting blocks are used to absorb machine vibrations through elastic hysteresis, as mentioned in Section 11.5, what becomes of the energy associated with the vibrations?

A horse is hitched to a wagon. Since the wagon pulls back on the horse just as hard as the horse pulls on the wagon, why doesn’t the wagon remain in equilibrium, no matter how hard the horse pulls?

If the velocity at each point in space in steady state fluid flow is constant, how can a fluid particle accelerates?

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?

During an auto accident, the vehicle’s air bags deploy and slow down the passengers more gently than if they had hit the windshield or steering wheel. According to safety standards, air bags produce a maximum acceleration of 60g that lasts for only 36 ms (or less). How far (in meters) does a person travel in coming to a complete stop in 36 msat a constant acceleration of 60 g?

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?