(2016)

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PHYSICSfamily name.)MarksName.

1. Suppose a system of three objects: a book, a table, and the earth. Let W be thegravitational force acting on the book lying on the table, N be the normal force acting
on the book from the table, P be the force with which the book pushes the table, and F
be the universal gravitation acting on the earth from the book. Answer the questions
below on the following pairs of the forces:(a) W and N (b) W and P (c) W and F (d) N and P (e) N and F (f) P and F.
(1) Which pairs of the forces do satisfy the action-reaction law? Choose two correct
answers from (a) - (f) and write the letter of your choice.

(1-1)

(1-2)
(2) Which pair of the forces is in the situation where the object is in equilibrium and nonet force is acting? Choose a correct answer from (a) - (f) and write the letter of yourchoice.

(2)12. The velocity v [m/s] of an object at time t [s] is given by v = – 4.0 + 2.0 t. Round off
your answers to two significant figures.
(1) Calculate the magnitude of the force F acting on the object of mass m = 4.0 kg.

(1)N(2) Calculate the kinetic energy K of the object of mass m = 4.0 kg at time t = 3.0 s.

(2)J(3) Setting the initial position x0 = 0.0 m of the object at time t = 0.0 s, calculate the time t(t > 0.0 s) at the position x = 21 m of the object.

(3)

2s

3. An object of mass m [kg] is vertically thrown upward along the positive direction
into the frictionless air. The object slows to rest and reaches at the highest point.
Afterwards, the object accelerates along the negative direction and falls straight down.
Let g be the magnitude of the gravitational acceleration.
(1) What is the force acting on the object just after the object is vertically thrown
upward? Choose a correct answer below from (a) - (c) and write the letter of yourchoice.
(a) – mg(b) 0(c) mg(1)(2) What is the force acting on the object at the instant when the object is at rest at thehighest point? Choose a correct answer below from (a) - (c) and write the letter of yourchoice.
(a) – mg(b) 0(c) mg(2)3

4. The displacement y [m] of a wave traveling in the positive x-direction is describedby time t [s] and position x [m] of a medium as y = 3.0 sin{2π (0.50 t – 0.25 x)}.
(1) Find the equation of the propagation of crest. Choose a correct answer below from(a) – (d) and write the letter of your choice.
(a) x = 2.0 t – 1.0(b) x = 2.0 t – 3.0(c) x = – 2.0 t – 1.0 (d) x = – 2.0 t – 3.0(1)(2) Find the displacement y [m] of the standing wave that is obtained by a superpositionof a wave 3.0 sin{2π(0.50 t – 0.25 x)} and a wave 3.0 sin{2π(0.50 t + 0.25 x)}.
Choose a correct answer below from (a) – (d) and write the letter of your choice.
(a) y = 6.0 sin(0.50πx) sin(πt)(b) y = 6.0 sin(0.50πx) cos(πt)(c) y = 6.0 cos(0.50πx) sin(πt)(d) y = 6.0 cos(0.50πx) cos(πt)(2)(3) Find the position of the node of the standing wave solved above. Choose a correct
answer below from (a) – (d) and write the letter of your choice.
(a) x = 0.5 m(b) x = 1.0 m(c) x = 1.5 m(d) x = 2.0 m(3)4

5. Suppose a system of monoatomic ideal gas in a cylinder with a piston as shown in
the figure. Answer the following questions. Round off your answers to two significant
figures.
cylinderideal gaspiston(1) The pressure p, the volume V, and the temperature T of the ideal gas at the initialstate were p1 = 1.0×105 Pa, V1 = 1.2×10 -4 m3, and T1 = 3.0×10 2 K, respectively.
Next, the external force F slowly pushed the piston. As a result, the pressure and thevolume at the final state changed as p2 = 1.2×105 Pa and V2 = 8.0×10 -5 m3.
Calculate the temperature T2 at the final state.

(1)K(2) The pressure p and the volume V of the ideal gas at the initial state were p = 1.5×105
Pa and V1 = 1.2×10 -4 m3. Next, the external force F slowly pushed the piston atconstant pressure. As a result, the volume changed as V2 = 8.0×10 -5 m3.
Calculate the work W of the external force F to the ideal gas.

(2)J(3) What is the molar specific heat cv of monoatomic ideal gas at constant volume? LetR be the gas constant of ideal gas. Choose a correct answer below from (a) – (f) andwrite the letter of your choice.
35R(a) 2(b) R(c) 2 R(d) 2 R(e) 2 R(f) 2 R(3)5

(4) The pressure p, the volume V, and the temperature T of the ideal gas at the initialstate were p = 1.0×105 Pa, V1 = 6.0×10 -5 m3, and T1 = 3.0×10 2 K, respectively.
Next, the volume and the temperature changed as V2 = 8.0×10 -5 m3 and T2 atconstant pressure. Calculate the amount of the heat Q to the ideal gas from theexternal system at this process.

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6J

6. Two positive charges qA = 2.0×10 - 6 C and qB = 8.0×10 - 6 C are located at thepositions A and B as shown in the figure. The distance L between the positions A andB is 1.5 m. Let the proportionality constant ke of Coulomb’s low (Coulomb’s constant)be ke = 9.0×10 9 N･m2/C2. Round off your answers to two significant figures.

L = 1.5 md = 0.50 mxDCAB
qB = 8.0×10 - 6 C

qA = 2.0×10 - 6 C(1) The resultant electric field is equal to 0 at the position C which is located on theline AB. Calculate the length x from the position A to the position C.

(1)m(2) Calculate the magnitude of the resultant electric field ED at the position D withlength d = 0.50 m from the position A. The position D is located on the line AB.

(2)

N/C

(3) Calculate the magnitude of the resultant electric potential φD at the position D.
Note that the electric potential at infinity is taken to be 0.

(3)

7V

7. An uniform magnetic flux density B = 5.0×10 -3 T is applied parallel to the z-axis
as shown in the figure. A particle with a positive charge of q = 1.6×10 -19 C and amass of m = 2.4×10 -30 kg moves in the y-direction with a speed of v0 = 4.0×10 5 m/s.
The particle enters the region where the magnetic field is applied. The particle moves
with the rotational motion on the x-y plane in the region due to the Lorenz force.
Round off your answers to two significant figures.
zv0
Byx(1) Calculate the magnitude of the Lorenz force F on the particle.

(1)N(2) Calculate the radius R of the rotational motion of the particle.

(2)m(3) Calculate the period T of the rotational motion of the particle. You can use π =
3.14.

(3)

8s