Download Edexcel Homework for Topic 10 (Rollercoasters and relativity

Edexcel Homework for Topic 10
(Rollercoasters and relativity)
Questions 1: Work
1. Three people do 2,000 J of work; what distance do they move if:
(a) person A exerts a force of 200 N?
(b) person B pushes with a force of 50 N?
(c) person C uses a force of 0.8 N?
2. How much work is done if:
(a) a man weighs 750 N and uses the stairs to climb 50 m
(b) a woman lifts a 400 N rucksack onto her back, a height of 1.2 m
(c) a pebble of weight 0.2 N is thrown 5 m into the air?
3. If a porter does 6,000 J of work carrying a 600 N box up a flight of stairs, and
each step is 20 cm high, how many steps are there in the flight?
4. A lorry takes 30 m to slow down and stop. If its brakes exert a force of
20,000 N, then:
(a) how much work do the brakes do
(b) what is the maximum amount of heat generated
(c) how much kinetic energy did the lorry have?
5. If a large elastic band has 8 J of energy stored in it, what is the maximum
height it could project a 2.5 N weight into the air?
Questions 2: Power
1. Calculate the power of an engine that can:
(a) do 1,200 joules of work in 4 seconds
(b) lift a 200 N weight through 30 metres in 12 seconds
(c) drive a car 500 metres in 25 seconds against air resistance of 3,000 N.
2. A machine has a power output of 500 kilowatts.
(a) How quickly will it do 4,000 kJ of work?
(b) How much work can it do in one minute?
3. What is the power used in the following?
(a) A man weighs 750 N and uses the stairs to climb 50 metres in 100 seconds.
(b) A woman lifts a 400 N rucksack onto her back, a height of 1.2 metres in four
seconds.
(c) A pebble of weight 0.2 N is accelerated in a time of 0.1 seconds and then
projected 5 metres into the air.
4. If a horse can do 746 J of work in one second then
(a) how much work can it do in one minute?
(b) how long would it take to do 20 kJ of work?
5. If water is pumped out of a 20 m well by a pump that can produce a power of 3
kW, how many litres of water can be lifted per second (one litre of water weighs
10 N)?
Questions 3: Kinetic Energy
1. Explain, using the words kinetic energy, work, thermal energy, why a car
travelling at 10 m/s (22.5 miles per hour) can brake in a quarter of the distance
needed by a car travelling at 20 m/s (45 miles per hour).
2. Calculate the kinetic energy of:
(a) a person of mass 70 kg running at 8 m/s
(b) a rabbit of mass 4 kg hopping at 15 m/s
(c) a ball bearing of mass 0.016 kg rolling at 3 m/s.
3. Calculate the speed of
(a) a 100 gram (0.1 kg) apple with a 800 mJ (0.8 joules) of KE
(b) a rugby player of mass 140 kg and a KE of 1,750 J
(c) a 360 mJ (0.36 J) bumble bee of mass 5 g (0.005 kilograms)
4. If a rock and a roller coaster both have 1 200 J of kinetic energy, what are their
masses if:
(a) the rock is falling at 10 m/s
(b) the roller coaster is moving at 0.2 m/s?
5. Extension:
A Ferrari V10 engine has a power output of roughly 574,000 Watts (770 brake
horse power). If the car has a mass of 605 kg then:
(a) how quickly can it, in principle, reach a speed of 40 m/s (90 miles per hour)
from a standing start
(b) why will it not, in practice, achieve this?
Questions 4: Potential Energy
1. Explain, using the words energy, work, potential, kinetic and velocity why a
roller coaster gets faster as it goes down a slope.
2. A boy on a bridge drops a stone into a river. If the stone drops 3.2 metres
before hitting the water and it has a mass of two kilogram:
(a) how much potential energy did it have before the drop
(b) how much did it lose during the drop
(c) where does the potential energy go
(d) what is the maximum possible velocity of the stone?
3. A roller coaster of mass five tonnes (5 000 kg) approaches a loop at a velocity of
25 m/s.
(a) What is its kinetic energy?
(b) How high would it be if all this KE were converted to PE?
(c) What is the maximum possible radius of the loop to avoid stalling? (Assume
the roller coaster is held onto the track by its wheels.)
4. If 30 tonnes per second (30,000 kg/s) of water flows from a reservoir down a
mountain side, a total height of 500 metres, then:
(a) how much potential energy does each tonne of water start with
(b) what is the rate at which energy is lost from the reservoir?
5. A spaceship of mass 50 tonnes (excluding fuel) is launched from the surface of
the Earth into orbit at a height of 300 kilometres and a speed of 8 km/s.
(a) What is its final KE?
(b) What is its final PE?
(c) What is its total energy in orbit?
(d) Why is the total energy used in the launch much greater than the final
energy of the spacecraft?
Questions 5: Electrical Energy
1. In an electric circuit energy is carried by the moving charge. The amount of
charge passing through a motor in a fixed time is called an electric current.
When the charge loses its energy, work is done and its voltage is reduced.
State the UNIT for each of the terms in italics.
2. How much work is done by a 12 V motor if it draws:
(a) 2 amps for 20 seconds?
(b) 50 milliamps (0.05 amps) for 20 minutes?
(c) 5 amps for 5 hours?
3. How long does it take to lift a 20 N weight through 6 metres using a
(a) a 24 V motor drawing 0.5 A
(b) a 240 V motor drawing 0.1 A
(c) a 12 V motor drawing 2.5 A?
4. A power station produces electricity at a voltage of 25 000 V.
(a) What current would be required to produce 720 kJ in 10 minutes?
(b) If the voltage were reduced to 240 V and the current increased to 7.5 A, how
long would it take to produce the same energy?
5. Extension:
If a 12 V battery has a ‘capacity’ of 20 amp hours this means that after it has
delivered its 20 amp hours its voltage will fall to an unusable level.
(a) How many joules of electrical energy could it supply at 12 V?
(b) How long could it supply 5 A current?
(c) If its voltage began to drop after 2 minutes, what current would it be
supplying?
Questions 6: Moving in circles
1. When a car turns a corner it can sometimes skid. Explain why, using the
words acceleration, velocity, friction, force and mass.
2. A bucket of water, total weight 50 N is spun around, at a constant rate, on a rope
so that it turns upside down. If the tension in the rope at the top is 10 N then
what is:
(a) the total force on the bucket at the top
(b) the total force on the bucket at the bottom
(c) the total force on the string from the bucket at the bottom
(d) the tension in the string when the bucket is at the bottom?
3. A roller coaster train loops a loop so that at the top of the loop the downward
acceleration is 12 m/s. The weight of the roller coaster is 80 kN.
(a) What two forces are acting on the train?
(b) What is the mass of the train?
(c) What is the total force on the train?
(d) What is the downward force of the track on the train?
(e) What is the upward force of the train on the track?
4. Bends in a roller coaster are always banked and when the train rounds a bend
you feel heavier. For each of these situations:
(a) what happens to your weight
(b) what happens to the force on you from your seat
(c) what is happening to your velocity
(d) why do you feel heavier?
5. Extension (hard):
When a spaceship orbits a planet it is always falling towards the planet. This
means that gravity is accelerating it downwards. As the spaceship moves
horizontally it does not get any closer to the planet. Suppose that in 1 second
an orbiting space ship falls 5 metres and is moving horizontally at 8 km/s.
(a) Why is the spaceship no closer to the planet after 1 second?
(b) What would happen in 1 second if the spaceship decreased its horizontal
velocity to 7 km/s?
(c) What would happen in 1 second if the spaceship increased its horizontal
velocity to 9 km/s?
Questions 7: Squashing Time and Space
1. Copy and complete the following sentences using some of the words or phrases
in itallics.
a) When two observers move ………. to each other each will see the
length of the other …….., and the clocks of the other running ……...
unchanged, lengthened, relative, fast, slow, sideways,
shortened, backwards, inverted, next
b) Events on trains which last a short time when the train is stationary
would take ......…………….. to happen when the train is moving.
more time, less time, forever, no time
c) The theory of relativity is only really relevant if the objects are moving at
......……………………………………………………….
close to the speed of sound, close to the speed of light, a slow speed, the
speed of a proton
2. If a moving space rocket is found to be 20% shorter than it would be when
stationary, then how much slower will its clocks be running?
3. If you are travelling at 80% of the speed of light, passing objects seem to be only
60% of their normal length. This means that durations of passing events seem to
be 1.66 times what the passing clocks say.
a) Find the new lengths of
i) a 150 metre long wall.
ii) a parked car, length 5 metres.
iii) a planet, diameter 12,700,000 metres.
b) Find the new durations of the following passing events
i) a 50 minute physics lesson .
ii) a man’s life, 75 years.
c) How much time in the passing world would elapse during a 50 minute
physics lesson in your moving spaceship?
Questions 8: Einstein and Relativity
1. Think about the following words and group them into increasing order of certainty
(some might have equal certainty)
guess, theory, fact, hunch, feeling, speculation, hypothesis, hope, fear
Give brief reasons for your choice.
2. Today we ‘know’ that matter is made up from very small particles known as
atoms yet this idea, first suggested by the ancient Greeks, was not fully accepted
until around the beginning of the twentieth century. We cannot see the individual
atoms but nearly all of chemistry can be explained using the idea. Write a short
explanation of why you think people might not have wanted to accept the idea of
atoms.
3. One current scientific theory is that the Earth’s atmosphere is slowly heating up
because human beings are adding too much ‘greenhouse gas’ to it. Scientists and
others are still arguing about whether this theory is true. What facts do you think
would have to be established before you could decide one way or the other? Write
a list of facts that would convince you the theory was true, and another that would
convince you that the theory was false.
4. A Thought Experiment: Imagine that you came up with the theory that when an
object cools down it is because it has absorbed ‘coldness’ from its environment,
and that when an object heats up it is because it is losing its coldness. Use your
theory to explain how the sun heats the earth during the day and how the earth gets
colder during the night. Do you think this theory is as good as the one you have
been taught?
5. Research Activity: Einstein, in his relativity theory, suggested that some strange
ideas were actually true; for example that space and time can be squashed, that
matter cannot reach the speed of light and that mass and energy are equivalent
substances. Scientists before him had also suggested strange ideas, for example
Galileo suggested that without air resistance all objects would fall with the same
acceleration.
Find out about (using the library or internet) one of the following ideas and write a
short paragraph or two explaining why the idea came to be accepted.
The ‘Heliocentric Theory’
http://csep10.phys.utk.edu/astr161/lect/retrograde/copernican.html
Newton’s First Law of Motion
http://www.glenbrook.k12.il.us/gbssci/phys/Class/newtlaws/u2l1a.html
The Atomic Hypothesis
http://galileo.rice.edu/sci/theories/atomism.html
The Theory of Evolution by Natural Selection
http://www.pbs.org/wgbh/evolution/
The ‘Big Bang’ theory
http://liftoff.msfc.nasa.gov/academy/universe/b_bang.html
Teacher answers:
1: Work
1. a) 10 m
2. a) 37 500 J
3. 50
4. a) 600 000 J
5. 3.2 m
b) 40 m
b) 480 J
c) 2.5 km
c) 1.0 J
b) 600 000 J
c) 600 000 J
2: Power
1. a) 300 W
2. a) 8 s
3. a) 375 W
4. a) 44 760 J
5. 15
b) 500 W
b) 30 000 kJ
b) 120 W
b) 26.8 s
c) 60 kW
3: Kinetic Energy
2. a) 2 240 J
3. a) 4 m/s
4. a) 24 kg
5. a) 0.8 seconds
with road
b) 450 J
c) 72 mJ
b) 5 m/s
c) 12 m/s
b) 60 000 kg
b) lack of traction, gear changes needed, air resistance NOT friction
4: Potential Energy
2. a) 64 J
b) 64 J
3. a) 625 kJ
b) 31.3 m
4. a) 5 MJ
b) 150 MW
5. a) 900 000 MJ b) 150 000 MJ
lifted
c) 10 W
d) 8 m/s
c) 15.7 m
c) 1 050 000 MJ
d) Fuel must be also be
5: Electrical Energy
2. a) 480 J
b) 720 J
c) 1.08 MJ
3. a) 10 s
b) 5 s
c) 4 s
4. a) 48 mA
b) 400 s (6 min 40 s)
5. a) 864 kJ
b) 4 hours
c) 600 A
6: Moving in Circles
2. a) 60 N down
b) 60 N up
c) 110 N down
3. a) Reaction from track, gravity
b) 8 tonnes
c) 100 kN
d) 16 kN
4. a) stays the sameb) increases
c) changing
accelerating you towards centre of circle.
5. a) curved surface of planet falls away 5 m in 8 km
surface (⅛ of 5 m) c) 62.5 cm further from planet
d) 110 N
e) 16 kN
d) force from your seat is
b) 62.5 cm closer to
7: Squashing Time and Space
1. a) relative, shortened, slower
light
2. 17% (approx)
3. a) i) 90 m ii) 3 m iii) 7 620 000 m
c) 83 min 2 sec
b) more time
c) close to the speed of
b) i) 83 min 20 sec ii) 125 years
8: Einstein and Relativity
1. Fact is most certain, otherwise no real answers. Point out that ‘fact’ means
different things to different people. For some it’s ‘observed facts’, for others
‘well-established theories’.
2. Sceptical people would accept the possibility but would not be really convinced
until technology made such experiments feasible. This basically had to wait until
good vacuum pumps became available.
3. For example, need to establish fact of heating, fact that greenhouse effect works,
fact that emission of gases by humans is sufficient, fact (given warming) that no
other explanation works (eg solar cycles). To reject theory need to establish that
either there is in fact no warming or that if there is it is explained by eg lack of
recent volcanic activity (facts in climate and seismic records), or solar activity or
some effect not considered before.
4. Coldness leaves the earth during the day and travels towards the sun, cooling the
sun very slightly; but during the night all the coldness in space shines on the
Earth and is absorbed, making the earth cooler.
5.
Heliocentric: Explains all observed facts (eg phases of Venus) completely.
Newton’s First Law: People implicitly trust machines (eg aeroplanes) designed
using the law; this constitutes "proof".
Atomic Hypothesis: Explains nearly all observed facts (eg relative weights of
compounds and elements, gas pressure, Brownian motion), no credible
alternative.
Evolution: Favoured by circumstantial evidence (eg fossils, variety and
adaptation of species), but not proved.
Big Bang: No-one can think of anything better to explain eg cosmological
redshift and microwave background, unproveable?
In all cases reference to ‘scientific community’ as arbiters in accepting theories
should be made. Predictions of hitherto unobserved facts which turn out to be
true is psychologically very convincing, and examples could be given.