Download question 2 - Larbert High School

Higher Our
Dynamic Universe
QUESTION 1
Which of the following statements about vectors and
scalars is/are true?
a) Scalars have direction only.
b) Vectors have both magnitude and direction.
c) Speed is a scalar and velocity is a vector.
d) Distance is a vector and displacement is a scalar.
QUESTION 2
A car travels from X to Y in one hour 15 minutes and then
from Y to Z in one hour as shown in the diagram below.
Calculate or find:
a) Distance travelled.
b) Average speed
c) Displacement.
d) Average Velocity.
QUESTION 3
A long distance athlete runs from point P to point Q
and then jogs to point R. She takes 20 minutes to run
from P to Q and then 40 minutes to jog from Q to R.
Calculate or find:
a) Average speed of the athlete.
b) Average velocity of the athlete.
QUESTION 4
The diagram below shows the resultant of two vectors.
Which combination of vectors could produce this
resultant vector?
QUESTION 5
Which of the following contains one vector and two
scalar quantities?
QUESTION 6
How far from point X does the object hit the ground?
QUESTION 7
A helicopter is flying at a constant height above the
ground. The helicopter is carrying a crate suspended
from a cable as shown below.
QUESTION 8
Two cyclists X and Y choose different routes to travel from point
A to point B some distance away.
Cyclist X travels 10km due East followed by 14km on a bearing
of 210° in 90 minutes.
Cyclist Y travels directly from A to B ‘as then crow flies’ and
reaches point B at the same time as cyclist X.
Calculate or find:
a) Displacement from A to B.
b) Average velocity of cyclist X from A to B.
c) The average speed of cyclist Y if they reach point B at the
same time as cyclist X.
QUESTION 9
A ball is thrown vertically upwards from ground level.
When it falls to the ground it bounces several times
before coming to rest.
Which of the graphs below represent the motion of
the ball from leaving the throwers hand until it hits the
ground for a second time?
QUESTION 10
An LHS student sets up the apparatus in the diagram
below to measure the average acceleration of a
model car as it travels between P and Q.
QUESTION 11
Which of the following acceleration-time graphs represent the
same motion shown in the velocity-time graph?
QUESTION 12
A car accelerates uniformly from rest and travels a
distance of 60m in 6s.
Calculate the acceleration of the car.
QUESTION 13
A car is travelling at 30ms-1 when it is 50m from a
stationary lorry. The car moves in a straight line and
manages to stop just before it reaches the lorry.
a) Calculate the acceleration of the car.
b) What does the value calculated in a) tell us?
QUESTION 14
The velocity-time graph for the motion of an object
starting from rest is shown below.
Which of the following statements about the motion
of the object is/are true?
QUESTION 15
A lift in a hotel makes a return journey from the
ground floor to the top floor and then back again. The
corresponding velocity-time graph is shown below.
Sketch the associated acceleration-time graph
from the velocity–time graph shown above.
QUESTION 16
The acceleration-time graph for an object travelling in
a straight line is shown below.
Sketch the corresponding velocity-time graph
from the acceleration-time graph shown above.
QUESTION 17
QUESTION 18
A helicopter is descending vertically at a constant
speed of 3ms-1. A sandbag is released from the
helicopter and hits the ground 7s later.
Calculate the height of the helicopter above the
ground at the time that the sandbag was released.
QUESTION 19
A vehicle is travelling in a straight line.
Which pair of graphs could represent the motion of the vehicle?
QUESTION 20
QUESTION 21
An object starts from rest and accelerates in a
straight line. The graph below shows the objects
acceleration over a 5s time interval.
a) Calculate the velocity of the object after 5s.
b) Draw the velocity-time graph over the 5s.
c) Calculate the displacement of the object over the 5s.
QUESTION 22
A golfer strikes a golf ball which then moves off at an
angle to the ground as shown below.
The graphs below show how the horizontal and
vertical components of velocity vary with time.
Calculate or find:
a)Time to reach the maximum height.
b)Maximum height reached.
c)Horizontal range of the ball.
d)The resultant velocity of the ball on
impact with the ground.
QUESTION 23
The following velocity-time graph represents the vertical
motion of a ball over its 4s trajectory.
If the ball has a constant horizontal velocity of 15ms-1, then
calculate or find:
a)The angle that the ball is projected at.
b)Maximum height reached.
c)The horizontal range of the ball.
d)The resultant velocity on impact with the ground.
e) How can you tell that the vertical displacement is zero over
the balls trajectory from the information given?
QUESTION 24
A ball is projected with a horizontal velocity from a bench. The
ball travels a horizontal distance XY as shown below.
QUESTION 25
A cannonball is fired horizontally at 40ms-1 from the top
of a vertical cliff and hits a target. The height of the cliff
above sea-level is 80m as shown below.
Calculate or find:
a) Time taken for the cannonball to hit the target.
b) Horizontal displacement of the cannonball.
c) The resultant velocity of the cannonball at the instant that it
hits the target.
d) What assumption has been made in all of the calculations?
QUESTION 26
A golf ball is projected with a velocity of 24ms-1 at an
angle of 38° to the horizontal.
Calculate or find:
a)Initial horizontal and vertical components of velocity of the ball.
b)Time to reach the maximum height.
c)Maximum height reached.
The golf ball then hits the ground 15m below the maximum height
reached.
d)Calculate the horizontal displacement of the ball at this point.
(A sketch of the trajectory would be useful!!)
QUESTION 27
A golf ball is projected at an angle of 32° from the
horizontal with a velocity of 43ms-1.
Calculate or find:
a)The initial horizontal and vertical components of
velocity of the ball.
b)How long it takes the ball to travel from O to Q.
c)The horizontal distance travelled by the ball
from O to P and then from O to Q.
QUESTION 28
A javelin is thrown at 60° to the horizontal with a
speed of 20ms-1 and is in flight for 3.2s.
Calculate or find:
a)The initial horizontal and vertical components of
the javelins velocity.
b) The maximum height reached by the javelin.
c) Horizontal displacement of the javelin.
d) What assumption has been made in all of the
calculations?
QUESTION 29
A ball is fired vertically upwards from the top of a
launcher at 6ms-1 as shown in the diagram below. The
launcher has a constant horizontal speed of 1.5ms-1.
Calculate or find:
a) The time for the ball to reach its maximum height.
b) How far the maximum height is above the top of the
launcher.
c) The resultant velocity of the ball as it leaves the top
of the launcher.
QUESTION 30
The basketball in the diagram above is thrown with an initial
vertical velocity of 4.60ms-1 at an angle of 50° to the horizontal.
Calculate or find:
a)The initial horizontal component of velocity of the ball.
b)The time for the ball to reach the basket.
c) The height h at the top of the basket.
QUESTION 31
A hot air balloon of mass 350kg has people with a
total mass of 200kg on board.
Calculate the upthrust force acting on the balloon if it
accelerates upwards at 0.2ms-2.
QUESTION 32
A block of weight 1500N is dragged along a
horizontal road by a force of 500N.
Calculate the acceleration of the block if a force of
friction of 41N acts against the blocks movement.
QUESTION 33
A lunar landing craft descends vertically towards the
surface of the Moon while accelerating at -0.4ms-2.
If the craft and the crew have a total mass of 16,000kg
then calculate the upthrust force acting on the lunar craft.
(g = 1.6Nkg-1 on the Moon)
QUESTION 34
A tension force of 170N is applied vertically upwards
on a block of mass 15kg.
Calculate the acceleration of the block if the air
resistance acting against its motion is 11N.
QUESTION 35
A block of mass 4.0kg and a block of mass 6.0kg are
linked by a spring balance of negligible mass.
Calculate the total pulling force on the system if the
reading on the spring balance is 12N.
QUESTION 36
A horizontal force of 30N is applied as shown to two
wooden blocks that are in contact with each other.
If a frictional force of 5N acts against the motion of
the blocks then calculate the resultant horizontal
force acting on the 7kg block.
QUESTION 37
An LHS student performs an experiment to study the
motion of the lift in the STEM Academy going from the
second floor to the ground floor using bathroom scales.
QUESTION 37 (Cont’d)
The LHS student records the reading on the scales
at different parts of the lifts journey as follows.
Calculate or find:
a)The mass of the LHS student.
b)The initial acceleration of the lift.
c) Acceleration of the lift as it comes to rest.
QUESTION 38
A block of wood of mass 4kg accelerates down the
slope with an acceleration of 0.5ms-2.
Calculate the force of friction acting on the block.
QUESTION 39
A sledge is pulled a distance of 12m in a straight line
along a horizontal surface by a force of 80N acting at
28° to the horizontal.
Calculate the work done on the sledge by the rope.
QUESTION 40
A boat is pulled along a canal with an acceleration of
0.25ms-2.
Calculate the mass of the boat is the frictional force
acting on the boat is 41N.
QUESTION 41
A box of mass 20kg is pulled along a horizontal
surface with a force of 8.1N at an angle of 26° to the
horizontal.
Calculate or find:
a) The acceleration of the box if a frictional force of
1.28N is acting against its motion.
b) The horizontal distance travelled by the box in 6s.
QUESTION 42
A hot air balloon has a mass of 600kg. It is tethered
to the ground with two ropes, which make an angle of
25° to the vertical as shown below.
Calculate the tension in each rope.
QUESTION 43
The combined mass of a cycle and rider is 85kg.
The cyclist rides down the hill inclined at 15° with an
acceleration of 0.6ms-2. He then rides up another hill inclined
at 20° with an acceleration of 0.4ms-2.
Calculate or find:
a) The unbalanced force acting on the cyclist when
he is riding down the hill.
b) The unbalanced force acting on the cyclist when
he is riding up the hill.
QUESTION 44
An LHS student of mass 60kg on a sledge of mass
10kg slides down a slope which is 20° to the horizontal.
Calculate or find:
a) The component of weight of the student on the sledge acting
down the slope.
b) The initial acceleration if the force of friction acting is 14.6N.
c) How could it be possible for the student on the sledge to stop
accelerating and move with a constant speed instead?
QUESTION 45
A capsule on a fairground ride is held stationary with an
electromagnet, while the tension in the elastic chords is
increased using the winches. The capsule contains four
passengers and has a total mass of 400kg.
Calculate or find:
a)The tension in each chord if they have a vertical component of
tension of 4000N when held at 25°.
b) The initial acceleration of the capsule.
c) Show by calculation how the acceleration decreases as the capsule rises.
QUESTION 46
A car is designed with a ‘crumple-zone’ so that the
front of the car collapses during impact.
The purpose of the crumple-zone is to
QUESTION 47
Car manufacturers fit air bags which inflate
automatically during an accident, as shown below.
The purpose of the air bag is to protect the driver by
QUESTION 48
a) State the law of conservation of linear momentum
when it is applied to a collision between two objects.
b) Calculate the speed of car A if it runs into the back
of car B, with both cars joining together after the
collision with a speed of 15ms-1.
c) Show by calculation what type of collision is taking
place.
QUESTION 49
A block of mass 1kg slides along a frictionless surface at
10ms-1 and collides with a stationary block of mass 10kg.
a) If the 10kg block moves off at 1.5ms-1 then calculate the
velocity of the 1kg mass after the collision.
b) Which row in the table below is correct?
QUESTION 50
During a car safety check two cars are crashed
together on a test track. Car A has a mass of 1600kg
and car B has a mass of 1200kg.
a) Calculate the velocity of the cars if they lock
together after the collision.
b) Show by calculation what type of collision is
taking place.
QUESTION 51
The two vehicles below collide on a frictionless track.
Vehicle A has a mass of 0.25kg and vehicle B has a mass of 0.18kg. During
an experiment the vehicles collide and stick together with the computer
connected to the motion sensor displaying the velocity-time graph for vehicle A.
Calculate the velocity of vehicle B before the collision.
QUESTION 52
A shell of mass 6kg is travelling horizontally with a
speed of 240ms-1 when it explodes in two parts. One
part of mass 4kg continues in the original direction
with a speed of 120ms-1.
a) Calculate the speed of the other part of the shell and state
the direction that it is travelling in.
b) Show by calculation what type of collision is taking place.
QUESTION 53
A stationary golf ball is hit by a putter on a green as shown
below with an average force of 1.8N exerted.
The ball moves off with an initial velocity of 2.4ms-1 with the
time of contact between the putter and the ball being 80ms.
a) Calculate the unknown mass of the golf ball in grams.
b) Sketch a possible force-time graph for the impact of the
putter on the golf ball.
c) Which two quantities can be found using the force-time
graph?
QUESTION 54
A force is applied in a straight line to an object which
varies as shown in the graph below.
a) Calculate the impulse on the object over the 5s.
b) State the change in momentum in the object over
the first 4s.
QUESTION 55
The graph below shows the force which acts on an
object over an 8s time interval.
Calculate the change in momentum of the object
after 6s.
QUESTION 56
A force sensor is used to investigate the impact of a ball on a
flat horizontal surface. The ball has a mass of 40g and is
dropped vertically from rest through a height of 1.8m.
a) Calculate the magnitude of the impulse of the ball.
b) State the magnitude and direction of the change in momentum of the ball.
c) Calculate the speed of the ball before it hits the force sensor.
d) Calculate the speed of the ball after it hits the force sensor.
QUESTION 57
A soft ball and a hard ball are dropped from rest from the same
height and hit a floor surface.
a) Sketch the force-time graphs for each ball on the same axes.
b) Explain these graphs using the following terms: Impulse,
change in momentum, average force exerted and time of
contact.
c) Apply the theory used above to explain why it is compulsory
to wear a helmet when riding on a motorcycle.
QUESTION 58
A bullet of mass 40g is fired horizontally into a sand filled box,
which is suspended from the ceiling by long strings.
The combined mass of the bullet, box and sand is 12kg.
After impact the box swings upwards to reach a maximum
height as shown below.
a) Calculate the maximum velocity of the box after impact.
b) Calculate the velocity of the bullet just before impact.
QUESTION 59
A geostationary satellite of mass 6000kg used by Sky, is in orbit
at a height of 35,800km above the Earths surface.
The mass of the Earth is 6x1024kg and the radius of the Earth is
6.4x106m.
Calculate the gravitational force acting on the geostationary
satellite due to the pull of the Earth.
QUESTION 60
A rock of mass 0.90kg falls towards the surface of a planet.
The graph below shows how the gravitational field strength
varies with the height h above the surface of a planet.
Calculate the height of the rock above the planet if it has a
weight of 1.8N.
QUESTION 61
A space probe of mass 5200kg is in orbit at a height of
3.90x106m above the surface of Mars
a) If the gravitational force between the probe and Mars is
4200N then calculate the mass of Mars.
b) Calculate the gravitational field strength of Mars at this
height.
QUESTION 62
Two small asteroids are 20m apart and have a gravitational
force acting between of 6.67x10-7N.
Calculate the mass of each Asteroid if one Asteroid has four
times the mass of the other Asteroid.
QUESTION 63
a) State what is meant by the ‘gravitational field strength’.
b) The gravitational field strength on the surface of
Saturn = 11.5Nkg-1.
The radius of Saturn = 57,397km
The mass of Saturn = 5.68 x1026kg
i) Use Newton’s Universal Law of Gravitation to show
that G = gr2/M.
ii) Show that the data given for Saturn agrees with this
law.
QUESTION 64
A spacecraft travels at a constant speed of 0.85c relative to the
Earth.
A clock on the spacecraft records a flight time of 5.5 hours.
Calculate the flight time of the spacecraft that a clock on Earth
would record.
QUESTION 65
A spacecraft is travelling at a constant speed relative to the
Moon.
The length of the spacecraft measured by an astronaut on
board is 220m.
Calculate the speed of the spacecraft in terms of the speed of
light (?c) if an observer on the Moon measures the length of
the spacecraft to be 180m.
QUESTION 66
The Lorentz Factor (Ɣ) is found in the formulae for Time
Dilation and Length Contraction in Special Relativity.
a)State the equations for Time Dilation and Length
Contraction and amend them to allow the Lorentz Factor (Ɣ)
to be substituted into the equation.
b)Demonstrate by calculation that the Lorentz Factor (Ɣ) is
only appreciable for speeds approaching the speed of light.
QUESTION 67
The distance from Earth to the other side of the Milky Way Galaxy is 52,000 light years.
A spacecraft of length 150m is sent from Earth on this journey and the distance
measured on the spacecraft is 40,000 light years.
Calculate or find:
a) Speed of the spacecraft relative to Earth.
b) Time taken in seconds for the spacecraft to reach the other side of the Milky Way
Galaxy by an observer on Earth.
c) Time taken in seconds for the spacecraft to reach the other side of the Milky Way
Galaxy by a clock on the spacecraft.
QUESTION 68
An ambulance drives along Bellsdyke Road and passes a
stationary observer on its way to the Forth Valley Hospital.
The ambulance is travelling at a constant speed of 19ms-1
and its siren emits sound at a constant frequency of 780Hz.
Calculate the frequency of the sound reaching the
observer when:
a) The ambulance approaches the stationary observer.
b) The ambulance passes the stationary observer.
QUESTION 69
A Scotrail express train passes through a station that it does not
stop at on its journey from Glasgow Queen Street to Larbert.
A stationary observer on the platform notices that the frequency
of the sound from the train changes at its comes towards and
then passes them while standing on the platform.
State and explain how the frequency of the sound changes
using a wavefront diagram.
QUESTION 70
The graphic below shows the two Hydrogen emission spectra.
A
B
a) State and explain which spectrum (A or B) is viewed from
Earth and which one is viewed from a distant star.
b) The wavelength on source A of 530nm corresponds to the
wavelength on source B of 450nm.
i) Calculate the Red Shift Ratio Z for the star.
ii) Calculate the speed of the Earth relative to the star.
QUESTION 71
a) Using the diagram below explain the difference between
blue shift and red shift.
b) How does the red shift ratio differ when comparing a red
shift and a blue shift?
c) Explain how a binary star is blueshifted when moving
towards Earth.
QUESTION 72
a) State Hubble’s Law listing all of the quantities and units
involved.
b) Use the Higher data sheet to state Hubble’s Constant.
c) From Hubble’s Law, sketch the graph which gives the
gradient found to be Hubble’s Constant.
QUESTION 73
a) What can Hubble’s Law show and what can it be used to
find?
b) A galaxy is moving away from Earth at 0.093c.
Calculate the approximate distance of this galaxy from
the Earth in metres.
QUESTION 74
A star is not a ‘Perfect Blackbody Radiator’, but its theory can
be applied to stars.
a) What assumptions have been made to apply the Blackbody
Radiator Theory to stars?
b) i) Sketch a graph of Radiation Irradiance v Wavelength for a star.
ii) State two pieces of information that this graph highlights.
QUESTION 75
Wien’s Displacement Law equation applied to Blackbody Radiation Theory
is λp x T = 2.898x10-3mK
a) State the relationship between the peak wavelength and the temperature
of a blackbody radiator such as a star.
b) Calculate the peak wavelength of radiation emitted from the Sun if it has
a temperature of 6000K.
c) i) State the name of the diagram below.
ii) State which three factors that this diagram can tell us about a star.
The End.