Calculations

Question 1

(1) The bullet is moving with a velocity of 170 m/s.
The mass of the bullet is 0.030 kg.
Show that the momentum of the bullet is about 5.0 kg m/s.

Answer 1

momentum = 0.03 × 170 (1)

Question 2

(3) The bullet collides with the wooden block and sticks in it.
The bullet and the wooden block move off together.
The mass of the wooden block is 0.80 kg.
Calculate the velocity of the wooden block and bullet immediately after the
collision

Answer 2

momentum before = momentum
after (1)
5.1 = 0.83 × v (1)
v = 6.1 (m/s) (1)

Question 3

(2) Calculate the minimum total energy of the photons produced when an
electron and positron collide

Answer 3

E = (2 ×) 9.1 × 10-31 × [3 ×108]^2 (1)

= 1.6 × 10-13 (J) (1)

Question 4

(1) The intensity of light, in W/m2
, passing through the surface
which is 2 m (area = 0.8 m2) from S is

Answer 4

2.5 ÷ 4

Question 5

(2) Calculate the power of the light passing through the surface which is 1m from S

Answer 5

P = 2.5 x 0.2
or
2.5 = P / 0.2 (1)
0.5 (W) (1)

Question 6

(3) A bright object is placed 47 cm away from a lens as shown in the diagram. A real image of the bright object is seen on a screen which is 20 cm away from the lens as shown. Calculate the focal length of the lens.

Answer 6

1/f = 1/47 + 1/20 (1)
0.071 (1)
14 (cm) (1)

Question 7

(1) The lens shown in the diagram has a focal length of 12.0 cm.
The power of the lens is

Answer 7

8.3 dioptre

Question 8

(4) An object is placed 8.5 cm in front of a converging lens of focal length 12.0 cm.
Calculate the image distance.

Answer 8

substitution (1)
1/12= 1/8.5 + 1/v
transposition (1)
(1/v) = 1/12 - 1/8.5
evaluation (1)
(1/v) = -0.034
Inversion (1)
v = -29(cm)

Question 9

(3) The cross-sectional area of an optical fibre is 6.3 × 10^–6 m2
The intensity of the light entering the optical fibre is 3.2 × 107
W/m2.
Calculate the power of the light entering the optical fibre.

Answer 9

substitution: (1)
3.2 × 107
= power/6.3 × 10-6
transposition (1)
(power) = 3.2 × 107
× 6.3 × 10-6
evaluation: (1)
200 (W)

Question 10

(2) The optical fibre cable in an endoscope has a refractive index of 1.70. Use the equation and the graph to calculate the critical angle for the optical fibre.
sin c= 1/n (c= critical angle, n= refractive index)

Answer 10

substitute and evaluate
(sin c) = 1/1.7
(sin c) = 0.59
(1)
from graph or calculation
c = any value between
 34° and 38°
(1)

Question 11

(1) The current in the vacuum tube is 7.0 mA.
The charge on an electron is 1.6 × 10–19 C.
The number of electrons colliding with the metal anode in one second is

Answer 11

4.4 × 1016 (1)

Question 12

(3) In order to produce X-rays which can penetrate the luggage, each electron
must have at least an energy of 1.4 × 10–14 J.
The charge on an electron is 1.6 × 10–19 C.
Calculate the accelerating potential difference which will produce electrons of this energy

Answer 12

substitution: (1)
1.4 × 10-14 = 1.6 × 10-19 × V
Transposition
(1)
(V) = 1.4 × 10-14 / 1.6 × 10-19
evaluation:
(1)
88 000 (V) /88 x 103 (V)/ 8.8 x
104
(V)

Question 13

(1) On the surface of the Earth the weather balloon has a volume of 9.1 m3
, when the
temperature is 0 °C and the pressure inside the balloon is 101 kPa.
At 30 000 m above the Earth, the temperature is –46 °C and the pressure inside
the balloon is 1.12 kPa.
Show that –46 °C is 227 K.

Answer 13

-46 + 273 (1)

Question 14

(3) On the surface of the Earth the weather balloon has a volume of 9.1 m3
, when the temperature is 0 °C and the pressure inside the balloon is 101 kPa.
At 30 000 m above the Earth, the temperature is –46 °C and the pressure inside
the balloon is 1.12 kPa.
Calculate the volume of the weather balloon when it is at a height of 30 000 m.

Answer 14

substitution:
(101x9.1)/273= (1.12xV2)/227(1)

Transposition
V2= (101x9.1x227)/ (273x1.12)(1)

evaluation:
682 (m3) (1)

Question 15

(1) The cross-sectional area of the capillary tube is 1.94 × 10–3 cm2
.
The volume of the column of trapped gas at 25qC is about

Answer 15

2.1 × 10-2 cm3

Question 16

(3) The gas is heated to 50qC.
The volume of the trapped gas at 50qC is 2.31 × 10–2 cm3
.
Calculate the volume of the trapped gas at 100qC.

Answer 16

Temperature conversion to K
50°C to 323K OR 100°C to 373K
(1)
Substitution
V1 = 2.31 x10-2 x 373
 323
(1)

Evaluation
2.67 x 10-2 (cm3
)
(1)

Question 17

(4) This lens has a focal length of –0.33 m.
An object is 0.50 m in front of the lens.
Calculate the distance of the image from the lens.

Answer 17

Substitution
 1 + 1 = 1
0.5 v -0.33 (1)
Transformation
 1 - 1
 -0.33 0.5 (1)
Evaluation
1/v = -3 -2 = -5 (1)
v = -0.2 (m)
(1)

Question 18

(3) The total energy of the two gamma rays produced is 1.6 × 10–13 J.
Calculate the total mass of the positron and electron before annihilation.
Thevelocity of light is 3.0 × 108 m/s.

Answer 18

BEFORE
positron charge is +1, electron
charge is -1 (+e and –e)
(1)
OR
total charge is zero before
(annihilation)
(1)
AFTER
gamma rays have no charge
(1)