Chapter 5: 4Q (page 206)
Question: Tarzan swings back and forth on a vine. At the microscopic level, why is the tension force on Tarzan by the vine greater than it would be if he were hanging motionless?
Answer
As the vine stretches more, that pulls up more Tarzan.
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You're driving a vehicle of mass 1350kgand you need to make a turn on a flat road. The radius of curvature of the turn is. The coefficient of static friction and the coefficient of kinetic friction are both 0.25.
(a) What is the fastest speed you can drive and still make it around the turn? Invent symbols for the various quantities and solve algebraically before plugging in numbers.
(b) Which of the following statements are true about this situation?
(1) The net force is nonzero and points away from the centre of the kissing circle. (2) The rate of change of the momentum is nonzero and points away from the centre of the kissing circle.
(3) The rate of change of the momentum is nonzero and points toward the centre of the kissing circle.
(4) The momentum points toward the centre of the kissing circle.
(5) The centrifugal force balances the force of the road, so the net force is zero. (6) The net force is nonzero and points two and the centre of the kissing circle.
(c) Look at your algebraic analysis and answer the following question. Suppose that your vehicle had a mass five times as big. Now what is the fastest speed you can drive and still make it around the turn?
(d) Look at your algebraic analysis and answer the following question. Suppose that you have the originalvehicle but the turn has a radius twice as large (152 m). What is the fastest speed you can drive and still make it around the turn? This problem shows why high-speed curves on freeways have very large radii of curvature, but low-speed entrance and exit ramps can have smaller radii of curvature.
You swing a bucket full of water in a vertical circle at the end of a rope. The mass of the bucket plus the water is .The center of mass of the bucket plus the water moves in a circle of radius. At the instant that the bucket is at the top of the circle, the speed of the bucket is 4 m/s. What is the tension in the rope at this instant?
A planet of mass orbits a star in a highly elliptical orbit. At a particular instant the velocity of the planet is , and the force on the planet by the star is . Find
In June 1997 the NEAR spacecraft , on its way to photograph the asteroid Eros, passed near the asteroid Mathilde. After passing Mathilde, on several occasions rocket propellant was expelled to adjust the spacecraft's momentum in order to follow a path that would approach the asteroid Eros, the final destination for the mission. After getting close to Eros, further small adjustments made the momentum just right to give a circular orbit of radius around the asteroid. So much propellant had been used that the final mass of the spacecraft while in circular orbit around Eros was only . The spacecraft took days to make one complete circular orbit around Eros. Calculate what the mass of Eros must be.
A rope is attached to a block, as shown in Figure 5.64. The rope pulls on the block with a force of, at an angle ofto the horizontal (this force is equal to the tension in the rope).
(a) What is thecomponent of the force on the block due to the rope?
(b) What is the component of the force on the block due to the rope?
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