Homework 1Acceleration, Scalars and Vectors
St Andrew’s Academy CfE Higher Physics
Our Dynamic Universe
Homework 1Acceleration, Scalars and Vectors
1.A lorry driver travelling east to west decelerates in a straight line at a constant rate from 12 ms-1 to rest in 4 s.
- Calculate the acceleration vector of the lorry.
- What was the average velocity during braking?
- What was the braking displacement of the lorry?
2.Classify the following quantities using a table with two headings ‘scalars’ and ‘vectors’.
3. A train is travelling east to west and inside one of the carriages a child rolls a ball directly across the carriage towards the northerly side of the carriage.
Seen from above, the resultant velocity of the ball is 13 ms-1 on a bearing of 293°.
(a)Draw a vector diagram
(b)What is the speed of the train?
(c)How fast does the child roll the ball across the carriage?
4.A car is travelling at 20 ms-1 and accelerates at 0.5 ms-2 for 8 s.
(a)What is the final speed of the car?
(b)What distance does the car cover in this 8 s.
5.A bicycle is travelling west at 5 ms-1 and decelerates in a straight line at
0.3 ms-2 for 20 m. What is the final velocity of the bicycle?
6.A ball is thrown 6 m vertically up in the air.
(a)What speed was the ball thrown up with?
(b)What time did it take to reach it s greatest height?
Homework 2Velocity Time Graphs
1.A toy manufacturer has recently developed a new line of high speed model trains. Describe an experiment to measure the acceleration of a model train using two light gate sensors and a computer timing interface capable of measuring three consecutive time intervals.
Your description should include:
(a)A sketch of the apparatus
(b)A list of measurements taken manually and by the computer
(c)How the acceleration would be calculated using these measurements.
2.Copy and complete the table below to describe the motion in the three velocity time graphs below. Include the words constant, increasing or decreasing in your descriptions.
Graph A / Graph B / Graph CVelocity / then
Acceleration / then
3 The displacement time graph below illustrates the journey of a model train in the positive direction left to right.
(a)What is the maximum velocity of the train?
(b)When is the train not moving?
(c)What is the velocity of the train from 11 to 15 seconds?
4.The velocity time graph opposite represents the motion of a girl running for a bus. She runs from a standstill at O and jumps on the bus at Q. Find:
(a)The steady speed she runs at.
(b)The distance she runs
(c)The acceleration of the bus
5.The velocity time graph below shows the motion of a motorcycle
(a)Calculate the total displacement from start to finish
(b)Calculate the average velocity
(c)Calculate the four accelerations during the journey and hence draw a
labelled acceleration time graph.
6.A ball is rolled, starting from rest along the frictionless track opposite.
(a)Sketch the speed /time graph of the ball (no numerical values are required)
(b)Sketch the associated acceleration graph under the v/t graph.
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Homework 3Dynamics
Take acceleration due to gravity ‘g’ as 9.8 ms-2
1.A ‘frictionless’ shunting locomotive of mass 40 000 Kg pushes a ‘frictionless’ carriage of mass 60 000 Kg so that they both accelerate at 0.2 ms-2.
(a)Draw a diagram to represent this
(b)What force must the locomotive produce to achieve this acceleration?
(c)What force must the locomotive exert on the carriage to accelerate it?
(d)The locomotive uses the same force to push two 60 000 kg carriages against a frictional force of 4000N. What is the initial acceleration of the whole train?
2.Four skiers, each of mass 80 Kg are roped together and the first one falls into a crevasse. Assume the connecting rope is of negligible mass and there is no friction.
(a)What is the weight of the fallen skier?
(b)What is the force accelerating the skiers?
(c)What total mass must this force accelerate?
(d)Show clearly the acceleration of the group is 2.45 ms-2.
(e)What is the tension in the rope pulling the final skier?
(f)The second skier also falls, what is the group’s new acceleration?
3.The forces acting on a 6 000 kg helicopter in flight are its weight, 64 000 N upwards lift, forward engine thrust of 5 kN to the right and horizontal friction of 2 kN acting to the left.
(a)Draw a diagram with all four forces labelled.
(b)Draw a second diagram with only the resultant horizontal and
vertical forces
(c)Draw an accurate scale vector diagram to find the single resultant
force vector acting on the helicopter.
Check your answer by trigonometry.
(d)Calculate the acceleration vector of the helicopter
4.A jeep of mass 600 kg is parked on a 20° slope. It accelerates at 2 ms-2 and then drives 5 m up the slope at a constant speed of 10 ms-1.
(a)What is the weight of the jeep?
(b)Draw a vector diagram showing the two components of the jeep’s
weight parallel and perpendicular to the slope.
(c)What forces are needed:
(i) from the tyres as friction to stop the jeep from slipping down the slope?
(ii) from the axles to support the jeep perpendicular to the slope?
(d)What unbalanced force is needed to accelerate the jeep at 2 ms-2?
(e)What drive force must the jeep’s engines produce to:
(i) accelerate the jeep up the slope at 2 ms-2?
(ii) drive it up at a constant speed of 10 ms-1?
5.In filming a car advert, a car is to be driven off a 10 m high cliff at a horizontal speed of 15 ms-1. The director of the advert wishes to calculate the distance from the cliff and the direction that the car will hit the ground. Calculate:
(a)the vertical component of the final velocity.
(b)the time taken for the car to reach the ground.
(c)the horizontal distance travelled.
(d)the resultant velocity of the car as it hits the ground
6.An arrow is fired with a velocity of 60 ms-1 at 15° above the horizontal. It lands on level ground.
(a)Draw a velocity vector diagram for the initial velocity.
(b)Calculate the vertical component of initial velocity
(c)Calculate the horizontal component of initial velocity
(d)Calculate the total time of flight
(e)Calculate the maximum height reached
(f)Calculate the total horizontal distance travelled by the arrow
Homework 4Energy Conservation
1.A mountain bike has a mass of 20 kg and is ridden by a rider of mass 70 kg down a slope of length 24 m and vertical drop 3.7 m. The cycle’s speed at the top of the slope is 5.8 ms-1 and she brakes evenly to reduce the speed of the cycle to 4.7 ms-1 at the end of the slope.
(a)Calculate the potential energy of the cycle and rider at the top of the slope
(b)Calculate the kinetic energy of the cycle and rider at the top of the slope.
(c)Calculate the kinetic energy of the cycle and rider at the bottom of the slope.
(d)Describe the energy changes during the course of the journey down the slope.
(e)Calculate the energy converted to heat by the cycles brakes.
(f)Show that the average braking force exerted by the brakes is approx. 158 N.
(g)Calculate the average speed of the cycle down the slope
(h)Calculate the time taken for the cycle to travel down the slope.
(i)Calculate the power rating of the brakes during this journey.
2.A goods lift raises a load of 45 kg up a displacement of 3.2 m vertically upwards in a time of 9.5 seconds. The mechanical output power rating of the lift is 225 W.
(a)Calculate the weight of the load on the lift.
(b)Calculate the potential energy gained by the load.
(c)Calculate the mechanical energy supplied by the lift
(d)Calculate the work done against friction
(e)Show that the frictional force opposing the motion of the lift is 227 N.
The lift motor fails and the only force resisting the weight of the load was the frictional force of 227 N
(f)Calculate the unbalanced force acting on the load and hence calculate the acceleration of the load as it falls.
(g)Calculate the time taken by the load to drop down the lift shaft if it accelerates at this rate.
3.In a feature film, a 1200 Kg car is driven off a 9 m high building at a speed of
8 ms-1 horizontally.
(a)Draw a labelled diagram of the event
(b)Calculate the potential energy of the car as it leaves the roof?
(c)What is the total energy of the car initially?
(d)What is the kinetic energy of the car when it lands?
(e)What speed does it hit the ground with?
Homework 5Momentum and Impulse
1.A fairground uses bumper cars of mass 80 Kg. Billy has a mass of 70 Kg and is driving his car at +9 ms-1 directly at Donna. Donna has a mass of 50 Kg but has ‘fine tuned’ her car to run at -11 ms-1. After the inevitable head-on collision, Donna’s car comes to a stop.
(a)Draw a labelled ‘before and after’ diagram to illustrate the above information.
(b)Show Billy’s speed after the collision is 0.53 ms-1and state the direction.
(c)Calculate the total kinetic energy before the collision.
(d)By calculating the kinetic energy after the collision, state whether the collision was elastic or inelastic.
(e)The collision lasted 0.1 s. By considering the change in momentum of Donna’s car what was the average force exerted by Billy’s car on Donna’s?
2.An unmanned space satellite has a mass of 200 Kg (including propellant) and is initially stationary. The satellite ejects 500 g of propellant at an average velocity of 100 ms-1 to the right.
What is the new velocity of the satellite as a result?[2]
3.A sports scientist is measuring the forces on a tennis racquet using the time of contact between the ball and the racquet. The tennis ball has a mass of 100 g and hits the racquet with a velocity of -9 ms-1downwards, it rebounds at 6 ms-1upwards. The time of contact is measured as 0.04 s.
(a)What is the change in momentum of the tennis ball?
(b)Calculate the impulse of the racquet on the ball
(c)What is the average force on the ball from the racquet?
The scientist knows that the force varies with contact time as shown in the graph.
(d)What is the peak force exerted by the racquet on the ball?
(e)What is the maximum force exerted
by the ball on the racquet?
(f) Sketch a graph you would expect for the same ball being hit with a softer racquet over a longer time of contact.
Homework 6 Cosmology
Speed of sound = 340 ms-1
Speed of light c = 3 × 108 ms-1
approximation for Ho = 2·3 × 1018 s1
1. A spacecraft is travelling at a constant speed of 0.95 c. The spacecraft travels at this speed for 1 year, as measured by a clock on the Earth.
(a)Calculate the time elapsed, in years, as measured by a clock in the spacecraft.
(b)Show that the distance travelled by the spacecraft as measured by an observer on the spacecraft is 2.8 × 1015m.
(c)Calculate the distance, in metres, the spacecraft will have travelled as measured by an observer on the Earth.
2. A spacecraft moving at 2.4 × 108 ms −1 passes the Earth. An astronaut on the spacecraft finds that it takes 5 × 10−7 s for the spacecraft to pass a small marker which is at rest on the Earth.
(a)Calculate the length, in m, of the spacecraft as measured by the astronaut.
(b)Calculate the length of the spacecraft as measured by an observer at rest on the Earth.
8.A jet aircraft engine emits a sound of frequency 1.4 kHz. If the jet is travelling towards the observer at 240 ms-1 calculate the frequency of the sound detected by a stationary observer.
7. A man standing at the side of the road hears the siren of an approaching fire engine. He hears a frequency of 1.34 kHz. The siren on the fire engine has a frequency of 1300 Hz.
(a)Calculate the speed of the fire engine.
(b)What frequency of sound would be heard as the fire engine moves away?
7.A distant star is travelling directly away from the Earth at a speed of 2·4 × 107m s1.
(a)Calculate the value of redshift for this star.
(b)A hydrogen line in the spectrum of light from this moving star is measured to be 443 nm. Calculate the wavelength of this line when it observed from a hydrogen source at rest on the Earth.
8.A line in the spectrum from a hydrogen atom has a wavelength of 489 nm on the Earth. The same line is observed in the spectrum of a distant star but with a longer wavelength of 538 nm.
(a)Calculate the speed, in m s1, at which the star is moving away from the Earth.
(b)Calculate the approximate distance, in metres and in light years, of the star from the Earth.
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