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Physics 140 — Homework Week #12 Due: Wednesday, Dec

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Physics 140 — Homework Week #12 Due: Wednesday, Dec. 2"¢

9.2: Forces on Charges in Magnetic Fields

9.3: Motion of a Charge in a Uniform Magnetic Field

vi,

 

1. An electron moves in the plane of the page and is subject only to a magnetic force. At

point A the electron is moving upwards with a speed of 8.1 x 10° m/s. Find...

 

. oa. — . AS B

a) The magnitude and direction of the magnetic field that will cause the electron to follow 1.0m

the path from A to B

b) The time required for the electron to move from A to B.

2(T). A proton beam emerges from a particle accelerator, moving horizontally at 1200 m/s and od.

enters a uniform magnetic field, traveling perpendicular to the field as shown in the figure. The Sf

beam travels a distance of 1.18 cm while in the field. What is the magnitude of the magnetic OB

field?

3. A 150-g ball containing 4.00 x 10° excess protons is dropped down a 125 m vertical mine shaft that has been

converted into a Physics experimentation facility. At the bottom of the shaft, the ball suddenly enters a uniform

horizontal magnetic field that has magnitude 0.250 T and points from North to South. Find the magnitude and direction

of the force that this magnetic field exerts on the ball just as it enters the field.

4(T). In the figure shown, an electron is accelerated from AV

rest through a potential difference AV; of 1.00 kV and enters a :

the gap between two parallel plates having separation d = ) Ho C=

20.0 mm and potential difference AV2 = 100 V, with the | a d tv

lower plate being the negative plate. The electron’s velocity my ——_——— !

is perpendicular to the electric field vector within the plates.

What uniform magnetic field, perpendicular to the page allows the electron to travel in a straight line through the gap?

5. A proton passes through a region with a uniform magnetic field given as follows: B= (1T?t+2Tj-1 Tk). Ata

particular instant, the proton’s velocity vector is given by: v = (2 i — 4—j +1 ~k). What is the magnitude of the

magnetic force that the proton is subject to?

6(T). An alpha particle has a charge q = 3.20 x 10° Cand moves with a velocity v = (2 =i +3 —j —1 —k) in a region

with both a uniform magnetic field and uniform electric field. The magnetic field is given by:

B= (2Ti+4Tf+1Tk) andthe electric field vector is E = (4-7 —1 —j — 2—k)

a) Calculate the net force on the particle in component-unit vector notation.

 

4

 

b) Your friend claims that the motion of the particle in this situation is helical with the particle PPPS I

moving in a spiral motion around the magnetic field lines with a constant period and pitch, as a io T IL \—— B

shown. Is he correct? Explain.


10.1: Angular Velocity and Acceleration

7(T). The figure below shows the angular velocity-vs-time graph for a speck of dirt moving on a car tire. How many

revolutions does the speck make in the first 4 seconds?

8 (rad)

w (rad/s) tor.

20

Ll

10 () ; | » OCs)

2 4 6 hs

() » fs) ~2m-

() | 2 3 5

8. The figure above shows the angular position-vs-time graph for a bicycle wheel. What is the wheel’s angular velocity at

a)t=1s,b)t=4s,c)t=/7s?

9. Arecord player rotates on a turntable at 45 rom. What are a) the angular velocity in rad/s, b) the period of the

motion?

10(T). A computer hard drive spins up from rest at t = O and its angular velocity is given by the following function:

rad rad rad ,

@ = 1.0—+25—~t—080—~—t

S S S

 

a) At what time (t > Q) is the hard drive again at rest?

 

b) What is the angular displacement of the hard drive from t = Oto the time you found in a?

 

c) What is the initial angular acceleration of the hard drive?

 

d) At what time does the angular acceleration switch signs (e. g. go from positive to negative)?

 

e) What is the maximum angular velocity of the hard drive during the interval from t = O to the time you found in a?

10.2: Rotation with Constant Angular Velocity

10.3: Relating Angular and Linear Quantities

11. An amusement park ride has a diameter of 5.0 m and turns once every 4.0 s. The operator shuts the ride down and it

slows, coming to a rest in 20 s.

a) Before slowing, what is the speed of a child riding on the rim?

b) How many revolutions does the ride make as it stops?

12(T). A long string is wrapped around a cylinder with a radius of 3.0 cm. The cylinder is initially at rest and is free to

rotate on an axle. The string is pulled with a constant acceleration of 1.5 m/s? until 1.0 m of string has been unwound.

What is the cylinder’s angular speed, in rpm, at this time?

13. A ceiling fan with consists of a number of blades having a length of 20 cm and extending out from the centre. The

fan is turning at a rate of 1 revolution per second. After it is shut off, the fan coasts to a stop in 25s

a) What is the speed of the tip of a blade 10 s after the fan is turned off?

b) Through how many revolutions does the fan turn while stopping?

c) Through what distance does a point at the end of the blade turn as the fan comes to a stop?



14(T). A circular saw blade with a radius of 0.120 m starts from rest and turns in a vertical e

plane with a constant angular acceleration of 2.00 rev/s*. After the blade has turned

through 155 rev, a small piece of blade breaks loose, it travels with a velocity that is

initially horizontal and equal to the tangential velocity of the rim of the blade. The piece

travels a vertical distance of 0.820 m to the floor. How far does the piece travel

horizontally from where it broke off the blade until is strikes the floor?

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