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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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Question: Tarzan swings from a vine. When he is at the bottom of his swing, as shown in Figure 5.63, which is larger in magnitude: the force by the Earth on Tarzan, the force by the vine (a tension force) on Tarzan, or neither (same magnitude)? Explain how you know this.
In outer space two identical spheres are connected by a taut steel cable, and the whole apparatus rotates about its centre. The mass of each sphere is . The distance between centres of the spheres is. At a particular instant the velocity of one of the spheres is and the velocity of the other sphere is . What is the tension in the cable?
When a particle with electric charge q moves with speed v in a plane perpendicular to a magnetic field B ,there is a magnetic force at right angles to the motion with magnetic qvB ,and the particle moves n a circle of radius r (see Figure 5.77). This equation for the magnetic force is correct even if the speed is comparable to the speed of light. Show that
even if is comparable to c.
This result is used to measure relativistic momentum: if the charge q is known, we can determine the momentum of a particle by observing the radius of a circular trajectory in a known magnetic field.
An engineer whose mass is 70kgholds onto the outer rim of a rotating space station whose radius is 14mand which takes 30sto make one complete rotation. What is the magnitude of the force the engineer has to exert in order to hold on? What is the magnitude of the net force acting on the engineer?
A child of mass 26kg swings at the end of an elastic cord. At the bottom of the swing, the child's velocity is horizontal, and the speed is 12m/sAt this instant the cord is 4.30mlong.
(a) At this instant, what is the parallel component of the rate of change of the child's momentum?
(b) At this instant, what is the perpendicular component of the rate of change of the child's momentum?
(c) At this instant, what is the net force acting on the child?
(d) What is the magnitude of the force that the elastic cord exerts on the child? (It helps to draw a diagram of the forces.)
(e) The relaxed length of the elastic cord is 4.22m. What is the stiffness of the cord?
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