Pure Physics

Javier 12 Feb 2019

Question

A circuit consists of three resistors, R1, R2 and R3, and two switches A and B, as shown in the figure.

Javier20190212-1.jpeg

The resistances between terminals X and Y is measured for different settings of the switches A and B. The results are shown in the table.

Javier20190212-2.jpeg

a) Determine the resistance of resistors R1, R2 and R3.

b) Switch A is now closed and switch B is open. Calculate the resistance between terminals X and Z.

Answer

a) From the first row in the table, when switches A and B are both open, the total resistance is 12Ω.

Assuming that X is positive and Y is negative, current will flow through the circuit as shown.

Javier20190212-3.jpeg

Hence, we see that:

Javier20190212-7.jpeg

From the second row in the table, when switch A is open and B is closed, the total resistance is 10Ω.

Assuming that X is positive and Y is negative, current will flow through the circuit as shown.

Javier20190212-4.jpeg

Hence, we see that:

Javier20190212-8.jpeg

From the third row in the table, when switch A is closed and B is open, the total resistance is 6Ω.

Assuming that X is positive and Y is negative, current will flow through the circuit as shown.

Javier20190212-5.jpeg

Hence, we see that:

Javier20190212-9.jpeg

Solving the equations:

Javier20190212-10.jpeg

we obtain

R2 = 4 Ω

R3 = 2 Ω

b) When switch A is closed and B is open, we need to find the total resistance between X and Z.

Assuming that X is positive and Z is negative, current will flow through the circuit as shown.

Javier20190212-6.jpeg
Javier20190212-11.jpeg

Enzo 13 Oct 2018

Question

A man stands between two walls. He clapped his hands once and hears two echoes – one after 0.500 s and the other 0.300 s after the first. If the speed of sound in air is 330 ms-1, what is the distance between the two walls?

Answer

The first echo comes from the sound that travels to the nearer wall and reflects back.

Enzo-20181013-1.jpg

The distance travelled by the sound is

Enzo-20181013-2.jpg


Since the sound travels twice the distance between the man and the nearer wall,

Enzo-20181013-3.jpg

The second echo comes from the sound that travels to the farther wall and reflects back.

Enzo-20181013-4.jpg

We can calculate the distance travelled by the sound and the distance between the man and the farther wall.

Enzo-20181013-5.jpg

Hence, the distance between the two walls can be found.

Enzo-20181013-6.jpg

Enzo 8 Jul 2018

Question

A molten alloy is made by mixing 450 g of molten cobalt of density 9.00 g/cm3 with 240 g of molten iron of density 8.00 g/cm3.

a) Calculate the density of the molten alloy in kg/m3. (An important assumption must be made to do this question.)

b) What is the assumption made in your calculation?

c)Suppose now a 150 cm3 molten alloy of cobalt and iron has a density of 8.74 g/cm3, calculate the volume of cobalt and iron in the alloy in cm3. (You may make the same assumption as in previous parts of the question.)

Answer

a) To find the density of the molten alloy, we need to find the total mass and total volume of the alloy.

We assume that the two metals do not react and that the total mass is the sum of their individual masses and the total volume is the sum of their individual volumes.

 

Enzo-01.jpg

b) We assume that the two metals do not react and that the total mass is the sum of their individual masses and the total volume is the sum of their individual volumes.

c) To find the volumes of iron and cobalt, we first need to find the mass of the molten alloy.

We can then write down the relationships between the total mass and the mass of the cobalt and iron.

Enzo-03.jpg

Similarly we can write down an expression for the volume of cobalt and iron.

Enzo-04.jpg

Since we know the density of iron and cobalt, we can use the density to link the masses to their respective volumes.

Enzo-05.jpg

Hence, the equation relating the total mass becomes:

Enzo-06.jpg

We can now solve the following simultaneous equations:

Enzo-07.jpg
Enzo-08.jpg

Caitlin 9 Apr 2018

Question

Two resistors R1 and R2 are connected up in a circuit as shown in the figure below.

When the switch S is open, the ammeter reads 1.0 A and the voltmeter reads 8.0 V.

When the switch S is closed, the ammeter reads 1.5 A and the voltmeter reads 6.0 V.

Determine the values of R1 and R2. Show your working clearly.

Question.jpg

Answer

When the switch S is open, the current only flows through R2.

The circuit can be simplified as shown:

Caitiln-01.jpg

We can calculate the value of R2 directly.

Caitiln-02.jpg

When the switch S is closed, the current flows through both R1 and R2.

We can calculate the resistance across XY:

Caitiln-04.jpg

Since R1 and R2 are connected in parallel and we know the resistance across XY,

Caitiln-05.jpg

Hence, R1 is 8.0 Ω and R2 is 8.0 Ω

James 25 Feb 2017

Question

A student flips a coin into the air. Its initial velocity is 8.0 ms-1. Taking g = 10 ms-2 and ignoring air resistance, calculate:

a) the maximum height, h, the coin reaches, [2]
b) the velocity of the coin on returning to his hand, [1]
c) the time that the coin is in the air. [2]

Answer

a) To easily solve the problem, the velocity-time graph has to sketched.

Since there is no air resistance, the acceleration will be constant at 10ms-2 downwards. This means that the graph is a straight line.

At the highest point, the velocity of the coin will be zero.

The maximum height is given by the shaded area below.

To find the area we first need to find the value of th. Since we are taking upwards to be positive, the acceleration is -10 ms-2.

b) Since the coin falls back down to the student, the distance travelled downwards must be equal to the distance travelled upwards.

This means that the two shaded areas must be the same.

By symmetry, the final velocity of the coin must be -8.0 ms-1.

c) Since the area of the shaded areas are the same, the time taken for the upward journey and the downward journey must also be the same.

Hence the total time taken is twice the time taken for the coin to reach the highest point.

James 29 Sep 2016

Question

Find the potential difference across the 2.0 Ω resistor.

Find the potential difference across the open gap in the circuit.

Answer

The easiest way to find the potential difference in this case is to assign values of potential at the various points.

We first start at the sides of the cell, A and B.

We can assign any value as long as the difference between A and B is 6.0 V and A is a higher value than B.

In this case, we choose A to be 7 V and B to be 1 V.

All connecting wires are assumed to have no resistance. This means that the value of potential at all points of the same wire are of the same value.

Hence, E has a value of 7 V and C has a value of 1 V.

Since the circuit is an open circuit and no current flows, from V = I R, the potential difference across the 2.0 Ω resistor is zero.

This means that the values of the potential at both sides of the resistor are the same.

From the diagram, we can see that the difference between the potential at C and D is 0 V.

Hence, the potential difference across the 2.0 Ω resistor is zero.

From the diagram, we can see that the difference between the potential at E and D is 6 V.

Hence, the potential difference across the open gap in the circuit is 6.0 V.

 

David 16 Aug 2016 - 2

Question

The figure below shows the path of ray X as it passes through a thin converging lens AB.

Draw light rays to find the position of the image formed and determine the focal length of the lens AB.

Answer

Firstly, ray X is used to find the position of the base of the image. Since ray X comes from the base of the object, it will form the base of the image. Hence, the image is located along the blue line shown below:

Next, the ray from the tip of the object that passes through the optical centre is drawn.

The intersection point of the ray and the blue line is the location of the tip of the image.

The blue line is removed and a ray parallel to the principal axis from the tip of the object is added. This ray bends at the lens and reaches the tip of the image. The focal point can be found and the focal length can now be obtained.

The focal length is 10.0 cm.

David 16 Aug 2016 - 1

Question

A rectangular block of wood rests on the ground as shown in the diagram below.


Which of the following is the easiest way for a force F to topple the block?

Answer

For each block we identify the pivot point and the perpendicular distance of force F from the pivot point.


We can see that the perpendicular distance for D is the greatest. Force F will produce the greatest moment for D, hence it will topple the easiest.

Answer is D.

David 08 May 2016 - 1

Question

To avoid an accident the brakes of a car travelling at 30 ms-1 were applied suddenly. If the driver has a mass of 80 kg and it takes 3.0 s for the car to decelerate to rest what is the average force exerted by the safety belt on the driver during deceleration?

Answer

We first calculate the acceleration of the driver.

The force by the safety belt provides the force that causes the deceleration.

Hence, the average force exerted by the safety belt on the driver is 800 N.

James 08 May 2016 - 1

Question

What does the following paragraph mean?

To improve the accuracy for measurement that is too small, measure a few together and then find the average. For example, if we are finding the density of a marble, we take the mass of eg 5 marbles and divide by volume of the 5 marbles – and not find the density of individual marbles. If we are finding the average diameter of a marble, we measure the length of eg 5 marbles in a straight line and then divide by 5 – and not find diameter of individual marble and take average.

Answer

When finding the measurement of a small quantity, it is more desirable to find the total quantity due to a few items and then divide to obtain the quantity of a single item.

For example, we have a stick which is 3.58854 cm long. When measuring the length using a ruler, we will obtain 3.6 cm because a ruler can only read to 0.1 cm.

However, if we take 10 identical sticks and join them end-to-end and measure, we can obtain a total length of 35.8 cm. By dividing, we can find the length of each stick.

We know that there are exactly 10 sticks, not 10.1 or 9.9, hence the value of 10 is infinitely accurate and precise. We can assume that it is correct to many significant figures. Hence, the limiting significant figures is due to the value 35.8.

Therefore, our final answer of 3.58 cm is to 3 significant figures.

This method allows you to obtain an answer to more decimal places than the limit of the measuring instrument.

We can proceed further and join 100 identical sticks together and get a value which is even closer to the true value of the length.

With 100 sticks, the total length measured would be 358.8 cm when using a measuring tape. Then, dividing to find the length of each stick,

However, once we join so many sticks together, there will be other factors contributing to an error in measurement. For example, we need to ensure that the sticks are identical, are joined in a straight line and there are no spaces between all the sticks.

 

David 07 May 2016 - 5

Question

38. The figure below shows a permanent magnet suspended from a spring placed right on top of an electromagnet.

What will happen to the permanent magnet once the switch S is turned on?

Answer

When the switch is closed, current will flow in the direction as shown by the arrows on the wires in the diagram below. Based on the right hand-grip rule, the magnetic field produced by the current will be as shown below.

This means that the top of the iron core will be a magnetic North pole and repel the North pole of the permanent magnet. Hence, the permanent magnet will be pushed upwards.

David 07 May 2016 - 4

Question

A stone is thrown vertically upwards with a velocity of 5.0 m/s. After time t, it reaches the original position. Neglecting air resistance, what is the time required for the ball to reach the highest position?

Answer

By conservation of energy, the final velocity of the stone will be 5.0 m/s downwards. We also know that the acceleration of the stone is constant at 10m/s2 downwards. Hence, we can sketch a velocity-time graph.

The displacement upwards from 0 to 0.5 t must be equal to the displacement downwards from 0.5 t to t since the stone returns to its original position.

By symmetry, the highest point must be at 0.5 t.

Hence, the ball takes 0.5t to reach the highest point.

David 07 May 2016 - 3

Question

12. A pendulum bob is released from rest at position X which is at a height h above its lowest position Y and then passes through position Z. Position Z is 0.4h above Y. Assuming air resistance is negligible, find the ratio of the speed of the bob at position Y to that at position Z.

Answer

By Principle of conservation of energy, the energy at points X, Y and Z are all the same. This means that we can express the speeds at Y and Z in terms of the gravitational field strength, g, and h.

Now, we can find the ratio of the speed at Y to the speed at Z.

Hence, the ratio is 1.29 : 1.

David 07 May 2016 - 2

Question

11. A block of mass 2.0 kg is released from rest at point P as shown in the figure below. It is found that the block finally comes to rest at point Q.

The length of the track PQ is 2.5 m What us the average value of frictional force acting on the block when it is moving from P to Q?

Answer

All the initial energy of the block was lost to work done against friction.

The average frictional force is 4.0 N.

James 02 Apr 2016

Question

The photo on the right shows a refrigerator. Explain why the freezer compartment is often located at the top of a refrigerator.

Answer

The air that is cooled in the freezer becomes denser and sinks. Warmer air flows in to be cooled. This creates a convection current which allows the entire refrigerator to be cooled more effectively.

*Note that this is an old design of a refrigerator. It is still commonly used in low-end refrigerators. The shelves are usually made of wires and allow air to circulate freely in the fridge. Most modern refrigerator have separate compartments and separate cooling systems for each compartments.

Clive 02 Mar 2016

Question

Fig 8.1 for physics question by Clive

On Fig, 8.1, sketch on the card the pattern of the magnetic field produced by the current in the wire. The detail of your sketch should suggest the variation in the strength of the field. Show the direction of the field with arrows.

Answer

A straight current carrying conductor will produce a circular magnetic field. The direction of the magnetic field can be determined by the right hand grip rule.

The direction of current is indicated by the thumb and the direction of the magnetic field is given by the fingers.

The magnetic field lines are closer together nearer the wire because the magnetic field is stronger nearer the wire.