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Chapter 2: Q 875865 2 4 (page 81)

Inordertopullasledacrossalevelfieldataconstantvelocityyouhavetoexertaconstantforce.Doesn’tthisviolateNewton’sfirstandsecondlawsofmotion,whichimplythatnoforceisrequiredtomaintainaconstantvelocity?Explainthisseemingcontradiction.

Short Answer

Expert verified

Thus,thisviolatesthefirstandthesecondlawsofthemotion.

Step by step solution

01

Significance of Newton’s first and second laws and friction

The first law states that an object moves with constant velocity unless resisted by an external force.

The second law states that the rate of the change of momentum is directly proportional to the applied force and the direction of the force.

Friction is the resistance provided by one surface to another surface during the movement of the surface.

02

Determination of the violation of the Newton’s first and second law

Inthisquestion,frictionisoneoftheleadingforcesactingonthesledwhilepullingit.However,frictionactsintheoppositedirectionoftheobject’smotionwhichsignifiesfrictioncancelsandcounteractstheforcesthatcausemotion.Hence,iteventuallyleadstosmalleraccelerationandreducednetforce.Hence,thatisoneofthemainreasonsforapplyingaconstantforce.

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Most popular questions from this chapter

A carbon resistor is 5 mm long and has a constant cross section of0.2mm2The conductivity of carbon at room temperature is σ=3×104perohm-m.In a circuit its potential at one end of the resistor is 12 V relative to ground, and at the other end the potential is 15 V. Calculate the resistance Rand the current I (b) A thin copper wire in this circuit is 5 mm long and has a constant cross section of 0.2mm2.The conductivity of copper at room temperature is σ=6×107ohm-1m-1.The copper wire is in series with the carbon resistor, with one end connected to the 15 V end of the carbon resistor, and the current you calculated in part (a) runs through the carbon resistor wire. Calculate the resistance Rof the copper wire and the potential Vatendat the other end of the wire.

You can see that for most purposes a thick copper wire in a circuit would have practically a uniform potential. This is because the small drift speed in a thick, high-conductivity copper wire requires only a very small electric field, and the integral of this very small field creates a very small potential difference along the wire.

(1) A spring of stiffness 13 N/m, with relaxed length 20 cm, stands vertically on a table as shown in Figure 2.36. Use the usual coordinate system, with +x to the right, +y up, and +z out of the page, towards you. (a) When the spring is compressed to a length of 13 cm, what is the unit vector L^? (b) When the spring is stretched to a length of 24 cm, what is the unit vector L^? (2) A different spring of stiffness 95 N/m, and with relaxed length 15 cm, stands vertically on a table, as shown in Figure 2.36. With your hand you push straight down on the spring until your hand is only 11 cm above the table. Find (a) the vector L^, (b) the magnitude of L^, (c) the unit vector role="math" localid="1668490124469" L^, (d) the stretch s, (e) the forcerole="math" localid="1668490004012" F→ exerted on your hand by the spring.

A playground ride consists of a disk of mass M=43kgand radius R=1.7mmounted on a low-friction axle (Figure 11.94). A child of mass m=25kgruns at speed v=2.3m/son a line tangential to the disk and jumps onto the outer edge of the disk.

(a.) If the disk was initially at rest, now how fast is it rotating? (b) What is the change in the kinetic energy of the child plus the disk? (c) where has most of this kinetic energy gone? (d) Calculate the change in linear momentum of the system consisting of the child plus the disk (but not including the axle), from just before to just after impact. What caused this change in the linear momentum? (e) The child on the disk walks inward on the disk and ends up standing at a new location a distance from the axle. Now what is the angular speed? (f) What is the change in the kinetic energy of the child plus the disk, from the beginning to the end of the walk on the disk? (g) What was the source of this increased kinetic energy?

On a straight road with the +x axis chosen to point in the direction of motion, you drive for 3 h at a constant 30 mi/h, then in a few seconds you speed up to 60mi/h and drive at this speed for 1 h.

(a) What was the x component of average velocity for the 4 h period, using the fundamental definition. Of average velocity, which is the displacement divided by the time interval?

(b) Suppose that instead you use the equation vavg,x=(vix+vfx)2. What do you calculate for the x component of average velocity?

(c) Why does the equation used in part (b) give the wrong answer?

Question: The following questions refer to the circuit shown in Figure 18.114, consisting of two flashlight batteries and two Nichrome wires of different lengths and different thicknesses as shown (corresponding roughly to your own thick and thin Nichrome wires).



The thin wire is 50 cm long, and its diameter is 0.25 mm. The thick wire is 15 cm long, and its diameter is 0.35 mm. (a) The emf of each flashlight battery is 1.5 V. Determine the steady-state electric field inside each Nichrome wire. Remember that in the steady state you must satisfy both the current node rule and energy conservation. These two principles give you two equations for the two unknown fields. (b) The electron mobility

in room-temperature Nichrome is about 7×10-5(ms)(Ns). Show that it takes an electron 36 min to drift through the two Nichrome wires from location B to location A. (c) On the other hand, about how long did it take to establish the steady state when the circuit was first assembled? Give a very approximate numerical answer, not a precise one. (d) There are about 9×1028mobile electrons per cubic meter in Nichrome. How many electrons cross the junction between the two wires every second?
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