Charges of the amount 45 nC/m (charge per length) are deposited at the surface of a long, straight metal wire of diameter = 2 mm in which the surrounding media is air.

(a) Which electric field and potential distribution exists
around the wire ?

(b) How large is the electric field and the surface charge density
at the wire's surface ?

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In a downhill ski race surprisingly little advantage is gained by getting a running start. This is because the initial kinetic energy is small compared with the gain in gravitational potential energy even on small hills. To demonstrate this, find the final speed and the time taken for a skier who skies 75.0 m along a 25

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A faulty model rocket moves in the xy-plane (the positive
y-direction is vertically upward). The rocket's acceleration has
components ax(t)=?t2 and ay(t)=???t, where ? = 2.50 m/s4, ? = 9.00
m/s2, and ? = 1.40 m/s3. At t=0 the rocket is at the origin and has
velocity v? 0=v0xi^+v0yj^ with v0x = 1.00 m/s and v0y = 7.00
m/s.

1. Calculate the velocity vector as a function of time.

2. Calculate the position vector as a function of time.

Express your answer in terms of v0x, v0y, ?, ?, and ?. Write the vector v? (t) in the form v(t)x, v(t)y, where the x and y components are separated by a comma.

What is the maximum height reached by the rocket?

What is the horizontal displacement of the rocket when it returns to y=0?

1. Calculate the velocity vector as a function of time.

2. Calculate the position vector as a function of time.

Express your answer in terms of v0x, v0y, ?, ?, and ?. Write the vector v? (t) in the form v(t)x, v(t)y, where the x and y components are separated by a comma.

What is the maximum height reached by the rocket?

What is the horizontal displacement of the rocket when it returns to y=0?

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Calculate the mass of the sun from the radius of the earth's
orbit (1.50×10^{11} m), the earth's period in its orbit,
and the gravitational constant G.

What is the density of the sun ? (The sun's radius is
6.96×10^{8} m). Notice how it compares with the density of
the earth.

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An isolated charged conducting sphere has a radius R = 14.0 cm. At a distance of r = 24.0 cm from the center of the sphere the electric field due to the sphere has a magnitude of E = 4.90 ✕ 104 N/C. (a) What is its surface charge density (in µC/m2)? µC/m2 (b) What is its capacitance (in pF)? pF (c) What If? A larger sphere of radius 30.0 cm is now added so as to be concentric with the first sphere. What is the capacitance (in pF) of the two-sphere system? pF

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1)suppose we start with an electron with zero initial velocity. Let ϝ be

the typical time it would take for our electron to hit an atom. We can use this as

an average time between collisions as the electron makes its way through the

material. What is the typical *velocity*
of the electron when it hits an atom?

2) It turns out that the velocity you just calculated is not a bad estimate of the drift

velocity, *vd*. Now, as we saw, there is
another way to write *vd*, namely

*J* = (❝*ne*)*vd* for electrons
(remember *J* = *i* / *A* for uniform current
density), where

*n* is the number of charge carriers
(electrons) per unit volume. Solve this for *|vd|*

and equate with what you got in (1).

3)In the above, you should have a J on one
side and an E on the other. Now J and E

are in another important equation from today. Given that, can you
find an

expression for the resistivity of the material, ??

4)Also, we just saw in lecture that R =
(L/A)?, where L is the length of the wire and

A is its cross-sectional area. So, what

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A 1.50 kg book is sliding along a rough horizontal surface. At
point *A* it is moving at 3.21 m/s , and at point *B*
it has slowed to 1.25 m/s .

Part A

How much work was done on the book between *A* and
*B* ?

Part B

If -0.750J of work is done on the book from *B* to
*C* , how fast is it moving at point *C* ?

Part C

How fast would it be moving at *C* if 0.750J of work were
done on it from *B* to *C* ?

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At an angle of 36.5deg with the horizontal, a ladder, with mass (m = 100.0 kg) rests on a frictionless wall and on the ground with a friction coefficient (μS).

a) What is the minimum value of the ladder-ground static friction coefficient if the ladder’s center of mass is located at a distance, 1/3 of its total length?

b) A boy, with mass (m = 45.0 kg), uses the ladder to retrieve a bag of 5 basketballs, each with mass (m = 0.625kg), that rests on the top of the wall. If the boy must return safely to the ground, what is the new static friction coefficient required?

c) What is the %DIFF in static friction coefficients between parts a) and b)?

d) What is the %DIFF in the magnitude of the force delivered by the wall between parts a) and b)?

e) If the boy travels at a constant velocity during his round trip travel to retrieve the ball, what is the total work done by gravity?

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Write a short paragraph on what you understand by a force field. Use gravitational and electric field concepts for your posting.

(ii) How is the concept of potential used in a force field?

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5.1 A car is traveling along a highway at 65 miles per hour. The road is horizontal (0% slope). If the wind resistance and rolling resistance at the wheels creates a combined resistive force of 950 N, what is the power (kW) developed at the rear wheels?

5.2 How much power (kW) must the car engine in problem 5.1 develop if the overall mechanical efficiency of the transmission and drive train is 94%?

5.3 Assume the car engine in problem 5.1 is operated on gasoline with an energy content of 113,500 Btu's per gallon, and that the thermal efficiency of the spark ignition engine and drivetrain is 28.6%. What is the fuel efficiency of the car in miles per gallon?

5.4 The car in problem 5.1 approaches a mountain and begins ascending a grade of 6.0%. If the car maintains an uphill speed of 70 miles per hour, how much additional power (kW) must be developed by the engine to overcome the change in elevation? Assume the car has a mass of 1400 kg.

5.5 Assume the car above is operated on a blend of 85% ethanol and 15% gasoline (E85). If the energy content of ethanol is 80,460 Btu's per gallon, what is the energy content of the E85 fuel (Btu/gal)?

5.6 Assume the overall thermal efficiency of the engine and drivetrain of the car above drops to 24.5% when operated on E85 fuel. What is the estimated fuel economy (km/L) of the car above when subjected to the uphill operating conditions above (Problem 5.4)?

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The women’s record for fastest serve is by Sabine Lisicki with
131 mph which is approximately 58.56 m/s. Suppose she
hit the ball at a height of 2.6 meters above the court at an angle
of 8 degrees **below** the horizontal.

a. How high will the ball be when it reaches the net which is 11.89 meters away from the baseline? Assume she hit the ball right above the baseline. Does it hit the net or cross over it if the net height is 0.91 meters at the center?

b. If she served the exact same way, but now with no net in front of her, how far from where she hit the ball would it land on the court?

c. How fast is the ball going right before it hits the court? Give the ball’s horizontal, vertical, and resultant velocity. With the resultant, make sure to give both its size and direction (angle and reference)

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A meterstick (L = 1 m) has a mass of m = 0.19 kg. Initially it hangs from two short strings: one at the 25 cm mark and one at the 75 cm mark.

What is the tension in the left string right after the right string is cut?

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Explain the relation between the induced electromotive force and the sectional area of the secondary coil, while the number of turns of the secondary coil keeps constant.

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A 2.00kg bucket containing 11.5kg of water is hanging from a vertical ideal spring of force constant 140N/m and oscillating up and down with an amplitude of 3.00 cm. Suddenly the bucket springs a leak in the bottom such that water drops out at a steady rate of 2.00 g/s.

**Part A**

When the bucket is half full, find the period of oscillation.

**Part B**

When the bucket is half full, find the rate at which the period is changing with respect to time.

**Part C**

Is the period getting longer or shorter?

**Part D**

What is the shortest period this system can have?

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