5. [G29.12] Part of a single rectangular loop of wire with

dimensions shown in the figure is situated inside a

region of uniform magnetic field of 0.650 T. The total

resistance of the loop is 0.280 Given that the loop

is moving at 3.40 m/s, calculate the induced emf and

current in the loop.

6. [S30.29] The value of the line integral of �⃑� around the closed path shown in the figure is 3.77 x 10-6 T m. What is I3?

7. [Optional] [G28.37] A wire is formed into the shape of two half circles connected by equal-length straight sections as shown in the figure. A current I flows in the circuit clockwise as shown. Determine the magnitude and direction of the magnetic field at the center, C.

Answer

1. 𝑎. 2.0 × 10−4𝑖̂ T 𝑏. 4.0 × 10−4𝑖̂ T 𝑐. 2.0 × 10−4𝑖̂ T 2. 360 A right; 360 A left 3. 35.9 A 4. - 5. 0.77 V; 2.76 A 6. 1A

7. �⃑� = −𝜇𝑜𝐼

4(

1

𝑅1+

1

𝑅2) �̂�

Part 2

8. [S9.36] The mass of the Earth is 5.97 × 1024 kg, and the mass of the Moon is 7.35 × 1022 kg. The

distance of separation measured between their centers is 3.84 × 108 m. Locate the center of mass of

the Earth-Moon system as measured from the center of the Earth.

9. [G9.77] Two people, one of mass 85 kg and the other of mass 55 kg, sit in a rowboat of mass 78 kg.

With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat,

3.0 m apart from each other, now exchange seats. How far and in what direction will the boat move?

[Hint: The centre of mass of the whole system (with respect to the shore) remains unchanged before

and after the exchange.]

10. [G10.41] A merry-go-round accelerates from rest to 0 68 rad/s. in 24 s. Assuming the merry-go-

round is a uniform disk of radius 7.0 m and mass 31,000 kg, calculate the net torque required to

accelerate it.

11. [G10.40] Calculate the moment of inertia of

the array of point objects shown in Fig. 10.40

about (a) the vertical axis, and (b) the

horizontal axis. Assume 𝑚 = 2.2 𝑘𝑔,𝑀 =

3.1 𝑘𝑔 and the objects are wired together by

very light, rigid pieces of wire. The array is

rectangular and is split through the middle by

the horizontal axis. (c) About which axis would

it be harder to accelerate this array?

12. [G10.51] An Atwood’s machine consists of two masses, 𝑚𝐴 and 𝑚𝐵 which are connected by a massless inelastic cord that passes over a pulley. If the pulley has radius 𝑅 and moment of inertia 𝐼 about its axle, determine the acceleration of the masses, 𝑚𝐴 and 𝑚𝐵 and compare to the situation where the moment of inertia of the pulley is ignored. [Hint: The tensions 𝐹𝑇𝐴 and 𝐹𝑇𝐵 are not equal.]

Selected Answers

8. 4.67 × 106𝑚 𝑓𝑟𝑜𝑚 𝐸𝑎𝑟𝑡ℎ′𝑠 𝑐𝑒𝑛𝑡𝑒𝑟. 𝑁𝑜𝑡𝑒 𝑡ℎ𝑎𝑡 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝐸𝑎𝑟𝑡ℎ 𝑖𝑠 6.37 × 106𝑚

9. 0.41 m towards initial position of 85 kg person

10. 𝜏 = 2.2 × 104𝑚.𝑁

11. (a) 6.6 𝑘𝑔.𝑚2 (b) 0.66 𝑘𝑔.𝑚2 (c) vertical axis

12. 𝑎 =(𝑚𝐵−𝑚𝑎)

(𝑚𝐴+𝑚𝐵+𝐼

𝑟2)g