# Physics 9702 Doubts | Help Page 145

__Question 715: [Dynamics > Momentum]__
A body of mass m, moving at velocity
v, collides with stationary body of the same mass and sticks to it.

Which row describes momentum and
kinetic energy of the two bodies after the collision?

momentum
kinetic energy

A mv
¼
mv

^{2}
B mv
1/8 mv

^{2}
C 2mv
½ mv

^{2}
D 2mv
mv

^{2}**Reference:**

*Past Exam Paper – June 2011 Paper 11 Q9*

__Solution 715:__**Answer: A.**

In any collision in a closed system
(such as this one), momentum should be conserved. That is, the sum of momentum
before collision should be equal to the sum of momentum after collision.

Sum of momentum before collision =
mv + m(0) = mv

After collision, mass of body = 2m.
Let the velocity after collision be u.

Sum of momentum after collision =
(2m)u = 2mu

From the conservation of momentum,

2mu = mv

Velocity u = v / 2

Momentum after collision = 2mu = 2m
(v/2) = mv

(The above momentum could be deduced
directly from the conservation of momentum, but the final velocity would be
unknown.)

Kinetic energy after collision = ½ (2m)
(v/2)

^{2}= ¼ mv^{2}

__Question 716: [Nuclear Physics]__
Nuclear reaction between two helium
nuclei produces a second isotope of helium, two protons and 13.8 MeV of energy.
Reaction is represented by the following equation.

^{3}

_{2}He +

^{3}

_{2}He - - - >

^{.........}

_{.........}He + 2

^{.........}

_{.........}p + 13.8 MeV

**(a)**Complete the nuclear reaction

**(b)**By reference to this reaction, explain meaning of the term

*isotope*.

**(c)**State quantities that are conserved in this nuclear reaction

**(d)**Radiation is produced in this nuclear reaction.

State

(i) possible type of radiation that
may be produced

(ii) why energy of this radiation
less than the 13.8MeV given

**(e)**Calculate minimum number of these reactions needed per second to produce power of 60W

**Reference:**

*Past Exam Paper – November 2012 Paper 22 Q7*

__Solution 716:__**(a)**{A = upper value, Z = lower value}

He: A
= 4 Z
= 2

p: A
= 1 Z
= 1

**(b)**The Helium produced and those reacting are isotopes since the

__nuclei__of both have 2 protons (same number of protons). The reacting Helium nuclei have 1 neutron while the one produced has 2 neutrons.

**(c)**

Proton number and neutron number

Energy – mass

Momentum

**(d)**

(i) Î³
radiation

{Î³ radiation is an EM radiation. It is neutral (uncharged) and do not
has mass. An alpha particle is a helium nucleus. It has a charge (+2) and some
mass. As stated in part (c), some quantities must be conserved in the nuclear
reaction. Since these are already conserved, we cannot add more mass, charge, …
The same applies for beta particles.}

(ii) The

__product__(s) must have some kinetic energy.**(e)**

Energy in Joules:

13.8MeV = 13.8 × 1.6×10

^{-19}× 10^{6}= 2.208×10^{-12}J
Power:

Let the number of reactions per
second be n

60 = n ×
2.208×10

^{-12}
n = 2.7(2) × 10

^{13}reactions s^{-1}

__Question 717: [Radioactivity]__
Scientists investigating count rate
from a radioactive source observed that the count rate fluctuates.

What do these fluctuations imply
about the nature of radioactive decay?

A It involves atomic nuclei.

B It is predictable.

C It is random.

D It is spontaneous.

**Reference:**

*Past Exam Paper – June 2013 Paper 11 Q38*

__Solution 717:__**Answer: C.**

Fluctuations in the count rate of a
radioactive source indicates the radioactive decay is random. It cannot be
predicted.

__Question 718: [Transformer]__
A transformer is illustrated in Fig.1.

**(a)**

(i) Explain why coils are wound on a
core made of iron.

(ii) Suggest why thermal energy is
generated in the core.

**(b)**

(i) State Faraday’s law of
electromagnetic induction.

(ii) Use Faraday’s law to explain
why potential difference across the load and the e.m.f. of the supply are not
in phase.

**(c)**Electrical energy is usually transmitted using alternating current. Suggest why transmission is achieved using

(i) high voltages,

(ii) alternating current.

**Reference:**

*Past Exam Paper – June 2011 Paper 41 Q6*

__Solution 718:__**(a)**

(i) To concentrate the (magnetic)
flux / reduce flux losses

(ii) The changing flux (in the core)
induces current in the core. The currents in core give rise to a heating effect.

**(b)**

(i) Faraday’s law of electromagnetic
induction states that the e.m.f. induced is proportional to the rate of change
of (magnetic) flux (linkage)

(ii) The magnetic flux is in phase
with / proportional to e.m.f. / current in primary coil. The e.m.f. / p.d.
across the secondary coil is proportional to rate of change of flux. So the e.m.f.
of the supply is not in phase with the p.d. across the secondary coil.

{For the primary coil, the
magnetic flux is proportional to the current while for the secondary, the
e.m.f. induced is proportional to the rate of CHANGE of flux. So, if the flux
is constant for the secondary, no e.m.f. is induced – it should be changing.
This is not the case for the primary. As long as there is an e.m.f. in the
primary, the magnetic flux is proportional to it – it does not need to be
changing.}

**(c)**

(i) For the same power
(transmission) {P = VI}, a high voltage is
transmitted with low current. With low current, there is less energy losses in
transmission cables {P = I

^{2}R}.
(ii) The voltage is easily /
efficiently changed.

{With a changing current,
the voltage can be easily changed.}

__Question 719: [Kinematics]__
Diagram shows a velocity-time graph
for a vehicle.

The vehicle, moving at 4.0 m s

^{–1}, begins to accelerate at time = 0.
What is vehicle’s acceleration at
time = 3.0 s?

A 0.67 m s

^{–2}B 1.0 m s^{–2}C 1.3 m s^{–2}D 2.0 m s^{–2}**Reference:**

*Past Exam Paper – June 2010 Paper 11 Q8 & Paper 12 Q9 & Paper 13 Q14*

__Solution 719:__**Answer: C.**

From a velocity-time graph, the
acceleration at time t is given by the gradient at time t. This gives the

**instantaneous acceleration**at that time.
In this graph, the gradient and
hence the acceleration is changing.

Note that the gradient at time t =
3s is obtained by drawing a tangent at that point and calculating its gradient.
We cannot just take the coordinate at that point (3, 6) to obtain acceleration
(as done for choice D).

A tangent at time t = 3s would pass almost
at/close to points (0, 2) and (6, 10).

Gradient = (10 – 2) / (6 – 0) = 8/6
= 1.33 ms

^{-1}

__Question 720: [Kinematics]__
The dotted line shows path of a
competitor in a ski-jumping competition.

Ignoring air resistance, which graph
best represents variation of his speed v with the horizontal distance x covered
from the start of his jump at P before landing at Q?

**Reference:**

*Past Exam Paper – November 2012 Paper 12 Q10*

__Solution 720:__**Answer: D.**

At the maximum height, speed v is
minimum (due to conservation of energy – gravitational potential energy is
maximum and kinetic energy is minimum) [A is
incorrect] but the speed of the jumper is not zero at the top of the
flight as he still has horizontal velocity. [C is
incorrect]

Just before landing (at maximum
value of x in graph), the speed is not zero. Since P is at point higher than Q,
the person has both potential energy and kinetic energy at P. From the
conservation of energy, kinetic energy is higher at Q (since Q is at a lower
height – the potential energy is converted into kinetic energy), and so, speed
v at Q must be higher than at P.

Due to acceleration due to gravity,
the change in speed v with x (i.e. the gradient) is not uniform. [B is incorrect]

For solution 720, why "Due to acceleration due to gravity, the change in speed v with x (i.e. the gradient) is not uniform."? I thought the acceleration is always constant so speed is constant?

ReplyDeleteThanks

Acceleration is the rate of change of velocity.

DeleteSo, a constant acceleration (and non-zero) means that the change in velocity is not zero. On other words, velocity is changing.

But if the velocity is changing uniformly? The what..can b be the answer

Deleteyeah, but this is not the case here.

DeleteIsn't the acceleration of free fall ignoring air resistance, 9.81ms^-2? Wouldn't that mean the change in speed is uniform hence B should be correct?

ReplyDeleteThe acceleration of free fall, with or without air resistance, is 9.81ms-1. Even if this acceleration is directed towards the surface, a body may still move upwards, if the resultant force on him is upwards, as in the case above.

DeleteNow, read the explanation above again, and more carefully.

Why for Question716, we cannot use 2(1.6×10-19 × 10^6 = 2.208×10-12 J

ReplyDeletesee below

DeleteFor question 416 (e), why we not need x2 when calculating the charges? The equation states there are 2 protons ah?

ReplyDeletecalculating the charges???? when did we calculate the charge?

Deleteif you mean the energy conversion from MeV to J, then we need to multiply of the charge of an electron, but that has nothing to do with protons.

So it means we always consider for charge of 1 electron ,no matter what questions?

DeleteYeah, for conversion of eV to J (it's only a conversion of units).

DeleteOf course, you should also account for the M. (I forgot to mention above)

Ok! Thank you. My doubt has been cleared finally.

ReplyDeleteIn Q 720 can we say that acceleration is not constant because altough one component of velocity is increasing unformly but the other is constant and for all projectile motions is the acceleration not constant

ReplyDeleteprojectile motion problems are solved by considering the 2 components: horizontal and vertical.

DeleteSince air resistance is ignored, the vertical acceleration is constant and the horizontal one is still 0.

So, the acceleration is still constant.

In question 20, resultant force will always be downwards and be 9.81 ms2

ReplyDeleteso should not there be constant acceleration ?

there is a constant accleeration but since this is a velocity-DISTANCE graph, the gradient does not represent the acceleration.

DeleteFurthermore, the motion is first upwards, then downwards.