Unit 1 : Mechanics and Heat. Homework 1 - Average and Instantaneous Speed.

Transcription

1 Homework 1 - Average and Instantaneous Speed. 1 Two pupils wish to measure the average speeds of cars as they travel between Craighall Crescent and Craighall Avenue. State what apparatus they would use, the measurements they would make and how they would be made. Also state how they would calculate the average speed from their measurements. 2 Show, using a labelled diagram, how you would measure the instantaneous speed of a trolley at the foot of an inclined plane. State the measurements taken and show how the instantaneous speed would be calculated from your measurements. 3 While traveling from Glasgow to Kilmarnock, the driver of a car looks at the speedometer and notices her speed as 90 km per hour. However, it takes 40 minutes to travel the 40 km journey. (a) (c) Calculate the average speed in km per hour. State two different occasions when the driver s instantaneous speed would be less than her average speed. Calculate what the driver s instantaneous speed of 90 km per hour would be in metres per second. 4 A plane leaves London Heathrow at 7.25 GMT and arrives in New York JFK at GMT. a) How long did the plane journey take? b) If it is 5100 km from London to New York, calculate the average speed in i. km per hour. ii. metres per second. c) The return journey takes 4 hours and 20 minutes.how does the average speed for the return journey compare with that of the outward journey? d) Suggest why the two average speeds are different. 1

2 5 A train is travelling from Glasgow to Edinburgh. Part of the train timetable is shown below : Station TimeDistance Glasgow dep Falkirk arr km dep Linlithgow arr km dep Edinburgh arr km (a) (c) Calculate the average speed in metres per second from Glasgow to Falkirk. Calculate the average speed in metres per second from Glasgow to Edinburgh. Give a reason why the average speeds calculated in (a) and are different. Total Mark = 20 2

3 Homework 2 - Vectors and Scalars 1 State the difference between a vector and a scalar quantity. 2 State the difference between distance and displacement. 3 State the difference between speed and velocity. 4 An orienteer ran 6 km North and then 8 km East. He ran on level ground and it took him 2 hours. (a) Calculate his average speed. Calculate his average velocity (give magnitude and direction). 7 A runner follows the path shown starting at A and arriving at B ten seconds later. 30m B 40m A a) What is the distance travelled by the runner? b) Calculate the the average speed of the runner. c) Calculate the runner s displacement (magnitude and direction). d) Calculate the average velocity of the runner (magnitude and direction). (5) 8 A runner runs on the perimeter of a square field as shown below : A 50m He starts at A and runs to C. (a) What distance has the runner travelled when he reaches C? Calculate the runner s displacement on reaching C (magnitude and direction). C Total mark = 14 3

4 Homework 3 - Acceleration 1 State what is meant by acceleration. 2 A cyclist takes 10 seconds to reach a speed of 14 m/s. Calculate the cyclist s acceleration. 3 Calculate the final speed of a rocket which accelerates at 200 m/s 2 from rest for 6.8 seconds. The speeds of supersonic aircraft and missiles are often stated in Mach numbers. The Mach number is the ratio of the speed of the body through air to the speed of sound in air. Express the final speed of the rocket as a Mach number if the speed of sound in air is 340 m/s. 4 A supertanker travelling at 14 m/s starts decelerating at 0.02 m/s 2. How long does it take to come to a complete stop? 5 For the following velocity-time graph : v(m/s) t (s) a) Describe the motions represented in parts A, B and C of the velocity-time graph b) Calculate the initial acceleration. c) Calculate the final deceleration. d) Calculate the total distance travelled. e) Calculate the average speed. f) Describe the motions represented in parts A, B and C of the velocity-time graph. (6) 4

5 6 A motorist joins a motorway at a speed of 25 m/s and accelerates up to a speed of 33 m/s in 4 seconds. He continues at this speed for 20 seconds and then has to brake to a standstill in 6 seconds because of a traffic jam. Draw a velocity-time graph of the motion described using graph paper. 7 a) If 1 km = 5 / 8 mile, calculate how many metres there are in 1 mile. b) Express 33 m/s in : i. km per hour, ii. miles per hour. c) Was the motorist in question 6 exceeding the motorway speed limit? Total mark = 20 5

6 Homework 4 - Forces, Mass and Weight 1 We cannot say what a force is, we can only say what a force does. State three things that forces can do. 2 A pupil is asked to measure the force required to pull a box along the floor and then to measure the force required to lift the box onto a table. (a) Newton (c) Describe how the pupil would measure these forces using a balance. Which of the forces would normally be greater? When the Newton balance measures forces, what is happening inside the balance. 3 What is weight? 4 What is the difference between mass and weight? Also state the units that each is measured in measured in. 5 State what is meant by gravitational field strength. 6

7 6 This information will be required in the following questions : Location Gravitational field Strength (N/kg) Earth 10 Mars 3.8 Jupiter 26 the Moon 1.6 outer space 0 (a) Calculate the weight on Earth of the following masses : (i) 10 kg (ii) 10,000 kg (iii) 100 g (iv) 1 g When the gravitational field strength changes, is it the mass or weight which remains constant? (c) Calculate the mass of objects with weights on Earth of : (i) 25 N (ii) 0.01 N (iii) 10,000 N (iv) N (d) : A man has a mass of 70 kg. Calculate what his weight would be (i) on Earth (ii) on the Moon (iii) on Mars (iv) on Jupiter (v) in outer space (5) Total mark = 20 7

8 Homework 5 - Friction and Forces 1 State what the force of friction does. 2. a) How does a sky diver increase the force of air friction acting on his body? Explain the situation. b) How does a car designer reduce the force of air friction acting on a car. Explain the situation. c) In a packing station boxes are pushed along a conveyer. How is friction reduced on the conveyer? Explain the situation. 3 Is force vector or scalar, and what unit is it measured in? 4 What are balanced forces. 5 Newton s First Law of Motion (Newton I) states that if no unbalanced force acts on a body then the body will remain at rest or move in a straight line with uniform speed. What does this tell us about what unbalanced forces do? 6 Newton s Second Law (Newton II) states that the unbalanced force acting on a body is proportional to the acceleration it produces; also, as the mass of the body accelerated increases, then the acceleration decreases for a given force. Write down a formula for Newton II, stating the quantities which the symbols represent and the units in which they are measured. 7 Define the Newton. 8

9 8 A liquid-fuelled rocket is taking off vertically upwards as shown below : Rocket: 5000 kg Thrusters: Each: 3000 kg Each delivering N thrust. a. What is the initial mass of the rocket? b. What is the initial unbalanced force acting on the rocket? c. Calculate the initial acceleration of the rocket. d. What happens to the mass of the rocket as it gains height? Why? e. What happens to the unbalanced force on the rocket as it gains height? What affect does this have on the acceleration? Total mark = 20 9

10 Homework 6 - Resultant Forces and Projectile motion 1 If two forces act in the same direction how do you find their resultant? 2 If two forces act in opposite directions how do you find the magnitude and direction of their resultant? 3 To find the resultant of two forces which act at right angles to each other a vector diagram must be drawn. How are the vectors representing the forces drawn? 4 Two forces at right angles to each other act on a rock as shown below : A 80N 80N 60N 60N B 80N 60N a. Which diagram(s) correctly show(s) the vector diagram for the resultant? b. Calculate the magnitude of the resultant force. 10

11 5 Considering a body of mass m falling freely, use Newton 2 to show that the acceleration due to gravity (g) in m/s 2 is equivalent to the gravitational field strength in N/kg. 6 Describe what a projectile is, explaining the curved path. 7 A ball is thrown out of a window with a horizontal speed of 10 m/s. At the moment it is released out of the window, the initial vertical speed is zero. It takes 4 s to reach the ground. (a) What is the value of the horizontal acceleration of the ball? State the final horizontal speed of the ball just before it hits the ground. (c) Sketch a speed-time graph for the ball s horizontal motion up to 4 s. (d) Calculate the total horizontal distance covered by the ball. (e) What is the value of the vertical acceleration of the ball? (f) Calculate the final vertical speed of the ball just before it hits the ground. (g) Sketch a speed-time graph for the ball s vertical motion. (h) Calculate the total vertical distance covered by the ball. Total mark = 20 11

12 Homework 7 - Newton s Third Law and Momentum 1 State Newton s Third Law. 2 Identify the Newton pairs in the following situations : (a) A swimmer swimming a length in a swimming pool. A car accelerating along a road. (c) An apple sitting on a table. (d) A cannon ball falling from the leaning tower of Pisa. (e) A rocket accelerating upwards from Earth. 3 What is momentum? What kind of quantity is it (vector or scalar)? 4 When two objects collide and the momentum of one of them decreases, what happens to the momentum of the other? Also, what happens to the total momentum before and after the collision? 5 Two 1kg vehicles on a linear air track collide. Vehicle A approaches vehicle B with a speed of 2 m/s while vehicle B is at rest. After the collision vehicle A is moving with speed 0.8 m/s. a) Calculate the velocity of vehicle B after the collision. b) Calculate the decrease in momentum of Vehicle A. c) Calculate the increase in momentum of Vehicle B. (5) 6 A trolley of mass 0.8 kg travelling with a speed of 2.4 m/s hits an identical trolley. Both trolleys stick together and move on. a) Draw a labelled diagram of the situations before and after the collision. b) Calculate the speed of the trolleys after the collision. Total mark = 20 12

13 Homework 8 - Work and Energy 1 State what work done is and the unit it is measured in. 2 What form of energy is work done changed into when : (a) A force does work against friction. A force does work against gravity. (c) A force accelerates a body. 3 A man exerts a force of 2 kn on a rock but doesn t shift it. How much work does he do? 4 A man has to exert an average force of 280 N to push a trolley round a supermarket. If he does 208 kj of work, how far does he walk? 5 State the relationship between work done, power and time, stating the units each are measured in. 6 State the relationships between : a) Gravitational potential energy (E p ), mass (m), gravitational field strength (g) and height (h). b) Kinetic energy (E k ), mass (m) and velocity (v). 7 A girl of mass 60 kg runs up a flight of stairs in 8.2 s. Each stair is 20 cm high and their are 50 stairs in the flight. a) What is the girl s weight? b) What is the total vertical height climbed? c) Calculate the potential energy gained by the pupil. d) Calculate the girl s power. 13

14 8 A sprinter can run 100 m in 12.2 s. He has a mass of 65 kg. a) Calculate the sprinter s average speed. b) Calculate the sprinter s kinetic energy when running at a speed equal to her average speed. c) Calculate the average power developed during the run. Total mark = 20 14

15 Homework 9 - Efficiency and Heat 1 Calculate the efficiency of a light bulb which uses 5400 J of electrical energy and gives out 1080 J of light. What happens to the missing 4320 J? 2 A power station is 42% efficient. If it produces 500 MJ of electrical energy per second, what is the input power to the station? 3 A solar cell is 8% efficient at changing the sunlight falling on it into electrical energy. (a) If the sunlight provides 2 kw/m 2 and the solar cell has an area of 7.5 m 2, how much electrical power is produced? Calculate the number of square metres of solar cell are required to give a power output equivalent to a 750 MW coal fired power station. 4 (a) What is heat and name the unit it is measured in? What is temperature and name the unit it is measured in? 5 If we had 0.5 kg of concrete, 0.5 kg of methylated spirits, 0.5 kg of aluminium, 0.5 kg of lead and 0.5 kg of water, what could be said about the quantities of heat required to change their temperatures by one degree Celsius? 15

16 In the following questions assume there is no heat loss, unless otherwise stated. Use the following value for specific heat capacities: Material Specific Heat Capacity (J/kg/ C) Water 4200 Methylated Spirit 2300 Aluminium 880 Copper Calculate the rise in temperature when 10,000 J of heat are supplied to 2 kg of water. 7 A 2 kw heater is used to heat a 3 kg block of aluminium for 3 minutes. Calculate the rise in temperature produced. 8 A 10 kg block of copper is at a temperature of 300 o C. As it cools it loses heat at a rate of 4000 J/s. Calculate what the temperature will be after 1 min 40 s. 9 A kettle with a 2 kw element contains 1 kg of water initially at a temperature of 10 o C. Assuming 80% of the heat produced by the kettle goes to heating the water, calculate: (a) (c) the heat the water needs to take in to reach its boiling point. the heat supplied by the kettle in this time. how long it takes to heat the water to boiling point. (4) Total mark = 20 16

17 Homework 10 - Latent Heat and Energy Conservation 1 Name the three states of matter. 2 What happens to the temperature of ice when it is melting? Does it gain or lose heat? Use the following data in the problems below Specific heat capacities: water 4200 J/kg/ o C ice 2100 J/kg/ o C Specific latent heat of fusion of ice : 3.34 x 10 5 J/kg Specific latent heat of vaporisation of water : 2.26 x 10 6 J/kg 3 You are given 2 kg of ice at 0 o C. (a) Calculate how much energy is required to melt all the ice without raising the temperature. (c) Calculate the energy required to bring the resulting water to boiling point. Calculate how much energy is required to change the water at its boiling point into steam at 100 o C. (d) What is the total energy required to change 2 kg of ice at 0 o C into 2 kg of steam at 100 o C (7) g of liquid ether are supplied with 2.8 x 10 5 J of energy and turned completely into a vapour. Calculate the latent heat of vaporisation of ether. 5 An electric kettle has a power rating of 2.8 kw. (a) Calculate how long it should take to bring 2 kg of water at an initial temperature of 20 o C to the boil. In practice it takes 4 m 30 s. (i) What is the energy lost to the surroundings? (ii) Calculate the efficiency of the kettle. 17

18 6 A space capsule with a mass of 1440 kg re-enters the Earth s atmosphere at 2000 m/s. The capsule has an average specific heat capacity of 1000 J/kg/ o C. a) Calculate the kinetic energy of the capsule on re-entry. b) If all the kinetic energy becomes heat energy of the capsule, calculate the final temperature of the capsule if it entered the Earth s atmosphere when its temperature was -250 o C g of water at a temperature of 10 o C are mixed with 400 g of water at 80 o C. (a) If the final temperature of the mixture is T o C, write down expressions for the heat gained by the cold water and the heat lost by the hot water. Calculate the final temperature of the mixture. (c) What have you assumed in your calculation in? Total mark = 24 18