# Physics 9702 Doubts | Help Page 16

__Question 85: [Forces > Resultant force]__Car of mass m travels at constant speed up slope at an angle θ to horizontal, as shown in diagram. Air resistance and friction provide resistive force F.

What force is needed to propel car at this constant speed?

A mg cos θ B mg sin θ C mg cos θ + F D mg sin θ + F

**Reference:**

*Past Exam Paper – June 2012 Paper 13 Q15*

__Solution 85:__**Answer: D.**

For constant speed, the forward force should be equal to the total backward force so that the resultant acceleration is zero.

Component of weight along slope = mg sin θ

Total backward force =

**mg sin θ + F**

Forward force needed = Total backward force = mg sin θ + F

__Question 86: [Waves > Intensity]__Sound wave consists of series of moving pressure variations from normal, constant air pressure.

Graph shows these pressure variations for two waves at one instant in time.

Wave 1 has intensity of 1.6 × 10

^{–6}W m

^{–2}.

What is intensity of wave 2?

A 2.4 × 10

^{–6}W m

^{–2}B 3.0 × 10

^{–6}W m

^{–2}C 3.6 × 10

^{–6}W m

^{–2}D 4.5 × 10

^{–6}W m

^{–2}

**Reference:**

*Past Exam Paper – June 2014 Paper 12 Q23*

__Solution 86:__**Answer: C.**

Intensity is proportional to amplitude square, A

^{2}.

For wave 1, amplitude A = 2 (from graph).

So, 2

^{2}= 4[units] corresponds to the intensity of 1.6x10

^{-6}Wm

^{-2}.

Wave 2, which has amplitude A = 3 (from graph), will have intensity corresponding to 3

^{2}= 9[units].

This (9 units) is equal to an intensity of (9/4) x 1.6x10

^{-6}=

**3.6x10**

^{-6}Wm^{-2}

__Question 87: [Resistance > Power]__Diagram shows low-voltage circuit for heating water in a fish tank.

Heater has resistance of 3.0 Ω. Power supply has e.m.f. of 12 V and internal resistance of 1.0 Ω.

At which rate is energy supplied to heater?

A 27 W B 36 W C 48 W D 64 W

**Reference:**

*Past Exam Paper – June 2014 Paper 13 Q35*

__Solution 87:__**Answer: A.**

Rate of energy supplied to heater = power in heater

**Power in heater = I**where R is the resistance of the heater.

^{2}RTotal resistance = 3.0 + 1.0 = 4.0Ω

Current = emf / total resistance = 12 / 4 = 3.0A

Power in heater = (3

^{2}) (3) = 27W

__Question 88: [Forces > Torque]__Four beams of same length each have three forces acting on them.

Which beam has both zero resultant force and zero resultant torque acting?

**Reference:**

*Past Exam Paper – November 2012 Paper 13 Q16*

__Solution 88:__**Answer: D.**

Torque is the moment of a torque. It causes a turning effect.

Consider A:

Upward force = 30 + 50 = 80N

Downward force = 90N

**Resultant force**= 90 – 80 =

**10N downward**

Resultant force is not zero. So, A is incorrect

Consider B:

Upward force = 36 + 70 = 106N

Downward force = 106N

**Resultant force**= 106 – 106 =

**0**

Consider forces acting about the centre of mass (where the 106N acts downwards),

Clockwise moment = 36 (50) = 1800Ncm

Anticlockwise moment = 70 (30) = 2100Ncm

**Resultant moment**= 2100 – 1800 =

**300Ncm**

Resultant moment is not zero. So, B is incorrect

Consider C:

Upward force = 28 + 35 = 63N

Downward force = 63N

**Resultant force**= 63 – 63 =

**0**

Consider forces acting about the centre of mass (where the 63N acts downwards),

Clockwise moment = 28 (50) = 1400Ncm

Anticlockwise moment = 35 (30) = 1050Ncm

**Resultant moment**= 1400 – 1050 =

**350Ncm**

Resultant moment is not zero. So, C is incorrect

Consider D:

Upward force = 42 + 70 = 112N

Downward force = 112N

**Resultant force**= 112 – 112 =

**0**

Consider forces acting about the centre of mass (where the 112N acts downwards),

Clockwise moment = 42 (50) = 2100Ncm

Anticlockwise moment = 70 (30) = 2100Ncm

**Resultant moment**= 2100 – 2100 =

**0**

Both the resultant force and the resultant moment are zero. So, D is correct

__Question 89: [Forces > Torque]__Two 8.0N forces act at each end of beam of length 0.60m. Forces are parallel and act in opposite directions. Angle between forces and beam is 60 °.

What is the torque of the couple exerted on beam?

A 2.4 N m B 4.2 N m C 4.8 N m D 9.6 N m

**Reference:**

*Past Exam Paper – June 2007 Paper 1 Q13*

__Solution 89:__**Answer: B.**

A couple consists of 2 forces, equal in magnitude and opposite in direction, acting on different points such that they produce a turning effect.

Torque of the couple, τ = F x d

where F is the magnitude of one of the forces and d is the perpendicular distance between the 2 forces

{We cannot use the distance as 0.60m since this is NOT the

__perpendicular__distance between the forces. + There is no need to identify any pivot since

__perpendicular distance between the 2 forces__is required.}

{Now, here is a working that was suggested (it is not a correct method to solve the question).

Consider the centre of the beam and try to calculate the corresponding length that would be perpendicular to the forces and pass through the origin. Let the perpendicular distance from the centre to 1 of the forces = x

x = 0.30 sin60

So, the total ‘resolved’ perpendicular distance between the 2 forces = 2 (0.30 sin60)

Torque, τ = F x d = 8.0 x 2 (0.30 sin60) = 4.156 = 4.2Nm

Even if the correct answer is obtained, this method is ‘physically’ incorrect because the beam is a ‘physical’ material with a ‘physical’ length, so we cannot resolve for another length that does not actually exist.

The correct what would be to resolve for the perpendicular (vertical) component of the forces. This is accepted since force is a concept (and this method is much easier and quicker). This is what is described next.}

Component of one force perpendicular to beam = 8sin60

Torque = 0.6 x 8sin60 = 4.157 = 4.2Nm

Can we do q86 with formula intensity = pressure x velocity ( velocity of sound will be constant for both in air ) .. But i am ending with answer a which wrong

ReplyDeleteYou need to work in terms of the amplitude here, as done above.

DeleteAlso, I don't know if that formula is correct anyway.

u better use this one

DeleteI=a^2*f^2

this will give u the value of f^2

which is constant for both u will get I putting value of a^2 and f^2

???

DeleteI don't know about this formula. What do a and f represent? Where did you get this formula.

Try to show the complete working.

This comment has been removed by the author.

ReplyDeleteWslm. Take the pivot to be at the centre of mass, then consider in which direction a force would cause the beam to turn.

DeleteCompare with the direction moved by the hands in a clock.

ok jazakallah

ReplyDelete