Physics Chapter on Motion & Energy

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Questions and Answers

After how many bounces will a ball of mass 0.1 kg, released from a height of 1.00 m, bounce no higher than 0.25 m?

What length of modelling clay is required to make a snowman consisting of two spheres, where one has a radius r and the other has a radius 2r?

12πr

What is the formula for the period of oscillation of a mass hung from a spring with a spring constant of k?

T = 2π√(m/k)

How long does it take for a ball, thrown at an angle of 30° from a height of 10 m, to hit the beach below?

2 seconds Signup and view all the answers

What is the average speed of the trams if 15 overtook a person walking at 1 m/s and 20 passed head-on during 1 hour?

1.67 m/s Signup and view all the answers

How long should it take Hayley and Rob to paint the house together if Hayley claims she can do it in 2 days and Rob in 3 days?

1.2 days Signup and view all the answers

What is the advantage of making observations simultaneously from the northern and southern hemispheres rather than two different locations in the UK?

Simultaneous observations from both hemispheres allow for more accurate measurements of the transit of Venus due to reduced parallax error. Signup and view all the answers

What distance was mentioned as the straight line distance between the two observation locations?

9560 km Signup and view all the answers

Calculate the distance between the Earth and Venus using the parallax angle of 0.0130° and the distance of 9560 km.

Distance = 9560 km / tan(0.0130°) Signup and view all the answers

What is the approximate value for 1 AU?

150 million km Signup and view all the answers

Calculate the orbital speed of Venus using the information provided.

Orbital speed calculations typically require the distance and time taken for one complete orbit. Signup and view all the answers

Why did the transit of Venus observed by Captain Cook last for several hours?

The transit lasted several hours due to the size of Venus relative to the angular size of the Sun, combined with the relative motion of the planets. Signup and view all the answers

How much work is done by the rider to increase their speed from 2.0 m/s to 6.0 m/s?

760 J Signup and view all the answers

Which graph shows the relationship between displacement from the start line and time for a marathon runner accelerating at a constant rate?

Graph B Signup and view all the answers

Which graph shows the resistance of a thermistor against current through the thermistor?

Graph C Signup and view all the answers

What are the corresponding changes in the wavelength and frequency of water waves when they travel from deeper to shallower water?

Wavelength decreases, Frequency decreases Signup and view all the answers

How long would a 2.5 kW kettle take to boil 1.25 L of water when used at 110 V?

6 ½ minutes Signup and view all the answers

Repeat readings in practical work are taken to:

Reduce the effect of random errors Signup and view all the answers

For the magnetic phenomenon demonstration with a bar, what must the bar be made of?

Soft iron Signup and view all the answers

What is the ratio of momentum between a golf ball (46 g) and a squash ball (23 g) if they have the same momentum?

2:1 Signup and view all the answers

What mass of Plutonium-238 is needed to provide a power of 100 W?

140 g Signup and view all the answers

What volume does the air from the tyre occupy after it is released at 1 atmosphere?

0.45 m³ Signup and view all the answers

How does using insulation with a thick solid foam core reduce heat loss from buildings?

It minimizes heat transfer through conduction and radiation. Signup and view all the answers

In a series circuit with a battery and two bulbs, what happens to the brightness of the bulbs?

The bulbs are not lit to full brightness. Signup and view all the answers

1 kilowatt-hour (1 kWh) is equivalent to ________ J.

3.6 × 10^6 Signup and view all the answers

Calculate the maximum energy that can be stored by the gravity battery.

Calculated based on mass, height, and gravitational potential energy. Signup and view all the answers

Calculate the speed at which the mass descends in the gravity battery system.

Calculated using power and energy formulas. Signup and view all the answers

How long can the gravity battery provide energy to the national grid at 800 kW?

Calculated using total energy available and energy required. Signup and view all the answers

Show that the maximum acceleration of the mass must be just less than 4 m/s².

Calculated using maximum tensile force and mass properties. Signup and view all the answers

Show that the cables are suitable for supporting the mass at a depth of 300 m.

Based on the calculated forces and ratios. Signup and view all the answers

What is Kepler's 3rd Law of planetary motion?

The square of the orbital period of a planet is proportional to the cube of the mean orbital radius. Signup and view all the answers

Calculate the mean orbital radius of Venus in astronomical units.

Calculated based on given orbital period. Signup and view all the answers

Study Notes

Bouncing Ball

A ball with a mass of 0.1 kg bounces on a hard surface and loses 25% of its kinetic energy with each bounce.
The ball is released from a height of 1.00 m.
We need to find out how many bounces it takes for the ball to bounce no higher than 0.25 m.

Snowman Model

A snowman is made from two spheres: one with radius r and the other with radius 2r.
The modelling clay is in the form of a cylinder with radius r/2.
We need to find the length of modelling clay required to make the snowman.

Spring Mass System

A mass m is hung from a spring with spring constant k.
The period of oscillation is given by the formula: T = 2π√(m/k)
We need to determine the period of oscillation in different scenarios:
- On a planet with a gravitational field strength of 2g.
- When two identical springs are connected end-to-end (in series).
- When two identical springs are connected side-by-side (in parallel).

Projectile Motion

A ball is thrown at an angle of 30° from the horizontal, with an initial speed of 10 m/s, from the top of a cliff 10 m high.
We need to find the time it takes for the ball to hit the beach below, assuming a gravitational acceleration of 10 m/s² and neglecting air resistance.

Tram Problem

A person walks down a street at a speed of 1 m/s for an hour, counting the number of trams passing by.
15 trams overtake the person, while 20 trams pass them head-on.
The trams follow a regular timetable in both directions.
We need to find the average speed of the trams.

Painting Job

Hayley can paint a house in 2 days, while Rob can paint it in 3 days.
They are both hired to work together.
We need to determine how long it will take them to complete the job together.

Intermediate Physics Challenge 2023

The 2023 Intermediate Physics Challenge is a competition for students.
The exam is 1 hour long and contains 3 sections (A, B, and C).
Section A has ten multiple choice questions each worth 1 mark. The section is worth 10 marks.
Section B has two short written answers, each worth 5 marks. The section is worth 10 marks.
Section C has two extended answer questions involving calculations, each worth 15 marks. The section is worth 30 marks.

Useful Constants and Equations

The density of an object is equal to mass divided by volume.
The wave speed of a wave is equal to the frequency multiplied by the wavelength.
For an ideal gas at a constant temperature, the pressure multiplied by the volume is equal to a constant.
The kinetic energy is equal to 1/2 multiplied by mass multiplied by the velocity squared.
The gravitational potential energy is equal to mass multiplied by gravitational field strength multiplied by height.
The gravitational field strength on Earth is approximately 9.8 N/kg.

Multiple Choice Questions

Question 1: The work done to increase a cyclist's speed from 2.0 m/s to 6.0 m/s is calculated using the work-energy theorem. The work done is equal to the change in kinetic energy. The answer is D. 1700 J.
Question 2: The displacement of an object accelerating at a constant rate can be calculated using the equation: displacement = initial velocity x time + 1/2 x acceleration x time squared. Given the information provided, the correct answer is B.
Question 3: The resistance of a thermistor decreases as temperature increases, and increases as the current increases. The correct answer is B.
Question 4: As water waves travel from deeper to shallower water, the wavelength decreases, and the frequency remains the same. The correct answer is B.
Question 5: The power of an electrical device is equal to the voltage multiplied by the current. The resistance of the kettle's heating element can be calculated using the equation: resistance = voltage squared / power. The time it takes to boil the water is inversely proportional to the power. The correct answer is D. 13 minutes.
Question 6: Repeat readings are taken to reduce the effect of random errors. The correct answer is A.
Question 7: The unknown material must be a ferromagnetic material that can be magnetized temporarily. The correct answer is A. Soft iron.
Question 8: Momentum is equal to mass multiplied by velocity. The ratio of the golf ball's velocity to the squash ball's velocity is 2:1. The answer is C. 2:1.
Question 9: Power is equal to the number of decays per second multiplied by the energy released per decay. The correct answer is C. 180 g.
Question 10: For an ideal gas at constant temperature, the volume is inversely proportional to the pressure. The correct answer is C. 45 m.

Short Written Questions

Question 11: Insulation reduces heat loss by reducing the rate of heat transfer. The foam core is a good thermal insulator, slowing down conduction. The foil surfaces minimize radiation heat transfer.
Question 12: The bulbs will not light up at full brightness in the incorrect circuit because the bulbs are connected in series. The current through the bulbs is the same, and since they have the same resistance, the total resistance is higher than in the parallel circuit. The voltmeter will read approximately 6 V, which is the total voltage of the battery.

Extended Numerical Questions

Question 13:
- 1 kWh is equivalent to 3.6 × 10 J.
- The maximum energy stored by the gravity battery can be calculated using the equation: energy = mass x gravitational field strength x height. The mass of the crushed rock can be calculated using: mass = density x volume. The volume of the cylinder is calculated using: Volume = pi x radius squared x height. The maximum stored energy is approximately 8.8 kWh.
- The speed at which the mass descends can be calculated using the equation: power = force x velocity. The force acting on the mass is equal to the weight of the mass. The speed is approximately 0.81 m/s.
- The time the gravity battery can provide power can be calculated using: time = energy / power. The time is approximately 11 seconds.
- The maximum acceleration of the mass can be calculated using: force = mass x acceleration. The maximum acceleration is approximately 3.9 m/s².
- The maximum weight of the cables can be calculated using: weight = mass x gravitational field strength. The mass of the cables can be calculated using: mass = density x volume. The volume of the cables can be calculated using: volume = pi x radius squared x length. The cables are suitable for supporting the mass, as their total weight is less than the allowed maximum tensile force.
Question 14:
- The mean orbital radius of Venus can be calculated using Kepler's 3rd Law: radius cubed is proportional to period squared. The radius of Venus's orbit is approximately 0.72 AU.
- Observations made from the northern and southern hemispheres provide a larger parallax angle, which leads to a more accurate determination of the distance to Venus.
- The distance between the Earth and Venus can be calculated using the parallax angle and the distance between the two observation locations. The distance is approximately 4.4 x 10 kilometers.
- Using the calculated distance between the Earth and Venus and the known value for the orbital radius of Venus (0.72 AU), the value of 1 AU can be calculated, which gives us approximately 150 million km.### Orbital Speed of Venus
Venus' orbital speed can be calculated using the provided information on its orbital radius and the gravitational constant.
Applying the formula for orbital speed (v = √(GM/r)), where G is the gravitational constant, M is the mass of the Sun, and r is the orbital radius of Venus, allows for the calculation.

Transit of Venus Duration

Ignoring Earth's motion, the transit of Venus lasts several hours due to the angular size of the Sun being approximately 0.5°.
This small angular size allows Venus to take several hours to cross the Sun’s disk.
Because Venus’s orbit is tilted slightly to the plane of the Earth’s orbit, it’s possible for Venus to pass in front of the Sun, providing us with a rare opportunity to observe this event.

Astronomical Unit

The transit of Venus played a key role in determining the astronomical unit (AU), the distance between Earth and the Sun.
The method used to determine the AU is more complex than initially presented and requires accounting for various factors, including the Earth's rotation, its motion, the planets' elliptical orbits, parallax, and more.
The AU value derived through early observations was remarkably accurate, within about 1% of today's accepted value, despite limited instrumentation at the time.
Since 2012, the AU has been defined as exactly 149 597 870 700 meters.

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Description

This quiz covers various physics concepts including the behavior of a bouncing ball, the dimensions required for building a snowman, and the period of oscillation of a mass-spring system. Additionally, it explores projectile motion principles. Test your understanding of these essential topics in mechanics!