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Chapter 7: Q. 22 (page 178)
A rope hangs from the ceiling. What is the tension at the midpoint of the rope?
The tension in the midpoint of the rope is.
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FIGURE Pshows two strong magnets on opposite sides of a small table. The long-range attractive force between the magnets keeps the lower magnet in place.
a. Draw an interaction diagram and draw free-body diagrams for both magnets and the table. Use dashed lines to connect the members of an action/reaction pair.
b. The lower magnet is being pulled upward against the bottom of the table. Suppose that each magnet’s weight is and that the magnetic force of the lower magnet on the upper magnet is . How hard does the lower magnet push against the table?
How does a rocket take off What is the upward force on itYour explanation should include an interaction diagram and free-body diagrams of the rocket and of the parcel of gas being exhausted.
A rocket burns fuel at a rate of , expelling the exhaust gases at a speed of relative to the rocket. We would like to find the thrust of the rocket engine.
a. Model the fuel burning as a steady ejection of small pellets, each with the small mass . Suppose it takes a short time to accelerate a pellet (at constant acceleration) to the exhaust speed . Further, suppose the rocket is clamped down so that it can’t recoil. Find an expression for the magnitude of the force that one pellet exerts on the rocket during the short time while the pellet is being expelled.
b. If the rocket is moving, is no longer the pellet’s speed through space but it is still the pellet’s speed relative to the rocket. By considering the limiting case of and approaching zero, in which case the rocket is now burning fuel continuously, calculate the rocket thrust for the values given above.
In case a, in the figure block A is accelerated across a frictionless table by a hanging weight . In case b, block A is accelerated across a frictionless table by a steady tension in the string. The string is massless, and the pulley is massless and frictionless. Is A’s acceleration in case b greater than, less than, or equal to its acceleration in case a? Explain.
A 70 kg tightrope walker stands at the center of a rope. The rope supports are 10 m apart and the rope sags 100 at each end. The tightrope walker crouches down, then leaps straight up with an acceleration of 8.0 m/s2 to catch a passing trapeze. What is the tension in the rope as he jumps?
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