James

James 27 Feb 2017 - 2

Question

A car travelling at a constant speed of 30 ms-1 passes a police car, which is at rest.

The police officer accelerates at a constant rate of 3.0 ms-2 and maintains this rate of acceleration until he pulls next to the speeding car. Assume that the police car starts to move at the moment the car moves past the police car.

What is the time required for the police officer to catch up with the car?

Answer

We assume that the police car catches up with the car at time t1.

The following formula for displacement can be obtained:

When the police car catches up with the car, both have travelled the same displacement.

The police car requires 20 s to catch up with the car.

James 27 Feb 2017 - 1

Question

A body is thrown vertically up from the ground with an initial speed u and it reaches the maximum height h at time t0.

What is the height it reaches at ½ t0?

Answer

We first define the upwards direction as positive.

When the body reaches the maximum height, the speed of the body is 0.

Knowing this, we can find expressions for h and t0. The acceleration of the body is taken to be 10 ms-2 downwards. Since we define upwards to be positive, the acceleleration will be -10 ms-2.

When the time is ½ t0,

Now that we know the speed at ½ t0, we can find the height travelled by the body.

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.

 

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.

 

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.