Mearns Castle
National 5 Physics

Dynamics and Space

Homework

 

To boldly go where no school has gone before

Velocity and Displacement
Useful Equation:

where:  v is the speed of an object (m s-1)
d is distance travelled by an object (m)
t is the time taken by an object to travel a distance (s)

where:  v is the speed of an object (m s-1)
s is displacement of an object (m)
t is the time taken by an object to be displaced (s)

1.   What is the difference between a scalar and a vector quantity?

2.   Put these quantities in to a table that shows whether they are vector or scalar:
force, speed, velocity, distance, displacement, acceleration, mass, time, energy.

3.   Copy and complete this table.

Distance / m	
Time / s	
Speed / m s-1	

100	
10		

30	
2.5		

510		
17	

72		
1.5	
	
30	
12	
	
0.3	
25	

(a)

(b)

(c)

(d)

(e)

(f)

4.   A person walks 25 metres west along a street before turning back and walking 15 metres east. The journey takes 50 seconds. What is the:
(a) Total distance travelled by the person?
(b) Displacement of the person?
 (c)  Average speed of the person?
 (d)  Average velocity of the person?

5.   An Olympic runner runs one complete lap around an athletics track in a race. The total length of the track is 400 metres and it takes 45 seconds for the runner to complete the race. Calculate the:
(a) Displacement of the runner at the end of the race.
(b) Average speed of the runner during the race.	
(c)  Average velocity of the runner during the race.

6.   An orienteer starts at point A, walks 300 metres north then 400 metres east until point
B is reached in a total time of 900 seconds, as shown.

400 m
B

300 m

A

(a) What is the total distance walked by the orienteer?
(b) What is the displacement of point B relative to point A?
(c)  What is the average speed of the orienteer?
(d) What is the average velocity of the orienteer?

7.   A car drives 15 kilometres east for 12 minutes then changes direction and drives 18 kilometres south for 18 minutes.
(a) What is the average speed of the car, in metres per second?
(b) What is the average speed of the car, in kilometres per hour?
(c)  What is the average velocity of the car, in metres per second?

8.   On a journey, a lorry is driven 120 kilometres west, 20 kilometres    north then 30 kilometres east. This journey takes 2 hours to complete.
(a) What is the average speed of the lorry, in km/h?
(b) What is the average velocity of the lorry, in km/h?

  9.	A car makes a journey from Castle Douglas to Stranraer along the A75 in 1    hour and 15 minutes. Use the map below to calculate the:
(a) Average speed of the car during the journey.
(b) Average velocity of the car during the journey.

10.   An athlete runs 8 km due west then turns and runs 6 km due north as shown in the diagram.

090˚

180˚

270˚

000˚

FINISH

6 km

START

8 km

a.  What is the total distance that the athlete travelled?
b.  By scale diagram or otherwise, find the resultant displacement of the athlete.
c.  The run was completed in 75 minutes.
    i.  Calculate the average speed of the athlete in km/h.
                     ii.  Calculate the average velocity of the athlete in km/h.

Average and Instantaneous Speed

1.	Explain the difference between average and instantaneous speed.

2.	State whether the following are average speeds or instantaneous        speeds.
a.  The speed of train travelling between Glasgow and Paisley. 
b.  The speed of a car on a speedometer.
c.  The speed of a roller coaster at bottom of a loop. 
d.  The speed of a car between two lamp-posts.
e.  The speed of a golf ball as it leaves the club.

3.	Describe a method of measuring the instantaneous speed of a trolley in the lab. Your description should include:
	a.  A diagram of the apparatus 
	  b.  The measurements taken
c.  Any calculations involved.

4.	A train leaving Glasgow at 9.00 am arrives in Edinburgh at 10.15 am.
The distance is 84 km.
a.  Calculate the average speed in kilometres per hour. 
b.  Express the speed in metres per second

v

5.     A jet travels from London to New York at an average speed of 223 m/s.
The flight time is 7 hours.
Calculate the distance travelled by the jet.

6.	
A student carries out an experiment to measure the instantaneous speed of a toy car using the apparatus shown below.

computer

Light sensor

runway

Light source

The length of the trolley is 30 cm.
The time recorded on the timer is 0.15 s.
Use the measurements to calculate the instantaneous speed of the trolley.

7.   An extract from a train time table is shown below:

(a) What was the average speed for the whole journey?

(b) Between which two stations was the train going fastest?

(c) A section of the train 50 metres long takes 4.2 seconds to 
     enter a tunnel.
     Calculate the instantaneous speed of the train at this entry point.

(d) How could the value calculated in (c) be made more accurate?

Acceleration

1.	State the definition of acceleration.

2.	A Ford KA increases its velocity from 2 m/s to 16 m/s in 10s.
A Peugot 106 takes 8s to accelerate to 11 m/s from rest. 
Show by calculation which car has the greater acceleration.

3.	A car slows from 70mph to 30 mph in 5 s when taking the exit from a motorway.
a)	Calculate the deceleration in mph/s.
b)	If 1 mile = 1.6km, what is the deceleration in km/h/s?
c)	Calculate the deceleration in m/s2.

4.	During a game of ten-pin bowling, a player gives bowling ball an acceleration of 3 m/s2 for 1.2 s.
	Assuming the bowling ball was accelerated from rest, calculate  the final velocity of the bowling ball.

5.	A supertanker travelling at 13 m/s decelerates at a rate of 0.03 m/s2.
	How long does it take to come to a complete stop?

6.	A rocket accelerates at 5.2 m/s2 for 10 minutes to reach a final velocity of 6200 m/s. Calculate the initial velocity of the rocket.

Velocity-time graphs - 1

1.	The motion of a race car is recorded as follows:

Time
(s)	0	10	20	30	40	50	60	70	80	
Speed
(m/s)	5	5	20	35	50	50	50	25	0	

a.  Using the graph paper provided, draw a speed time graph of the race car’s journey.
b.  Using the graph you have drawn, describe the motion of the race car over the 80 seconds.
c.  Using the graph you have drawn, calculate
	i.  The acceleration between 10 and 40 s.
	ii.  The total distance travelled by the race car.
 	iii.  The average speed during the 80 seconds.

2.   The velocity-time graph shown below describes the motion of a ball which has       been thrown straight up into the air then allowed to fall to the  ground.

velocity (m/s)

-15

15

10

5

0
					   0.5		1	     1.5	  	  2	       2.5
-5

-10

           					 time (seconds)

a.  At what time does the ball reach its maximum height?
b.  Calculate the maximum height that the ball reaches. 
c.  Calculate the height from maximum to the ground.
d.  Use your answers to b. and c. to calculate the height above the ground that the ball was thrown from.

3. 	A woman is driving along a poorly lit section of the M8. Just as she   
  	 passes a sign indicating that the next exit is 400 m away she notices 
   	that a lorry has jack-knifed across the exit road.
  	A speed time graph of her journey from the moment she passed the exit 
  	sign is shown below.

 	(a) When does the woman apply the brakes?

 	(b) Why does she not brake as soon as she sees the accident?

 	(c) How far does she travel between seeing the accident and stopping?

 	(d) Re-draw the speed time graph of the journey which would have been  
      produced if the road had been wet.

4. Crash test dummies are placed in car seats mounted on car simulation 
    rigs and then projected towards crash barriers during seat belt trials. 
    A speed time graph of the trial is plotted.

Use the graph to find out:

(a) when the car strikes the barrier

(b) the acceleration of the car before it strikes the crash barrier

(c) the length of the test track.

Velocity-Time graphs-2

1.   For each of these velocity-time graphs, describe the motion of the vehicle.

(a)	v

(b)	v

0	t	0	t

(c)	v

(d)	v

0	t	0	t

2.   Plot a velocity-time graph from each of these sets of data.

Time / s	Speed / m s-1	
0	10	
0.5	8.75	
1	7.5	
1.5	6.25	
2	5.0	
2.5	3.75	

(a)	(b)

Time / s	Speed / m s-1	
0	0	
1	1.5	
2	3.0	
3	4.5	
4	6.0	
5	7.5	

3.   Calculate the size of the acceleration of the vehicles represented by these velocity-time  graphs.

(a)	12

(b)

v / m s-1

v / m s-1

6.8

0

t / s

3.0

0
t / s

0.85

(c)

1.8

(d)	16

v / m s-1

v / m s-1

0.3	4

0

t / s

0.5

0		4 t / s

4.   Calculate the magnitude of the displacement of the vehicle represented by these velocity-time graphs.

(a)	16

(b)

v / m s-1

v / m s-1

4.5

0

(c)

t / s

7.0

0

(d)	16

t / s

2.8

v / m s-1

3

v / m s-1

4

    0	  7	 18
t / s	

0	3.0

6.0 t / s

8.5

5.   A ball is bounced off a surface. The velocity-time graph of the ball is shown.

v / m s-1

C

D 

0	
t / s

E 

A

B

(a) Describe the motion of the ball at each point indicated on the graph.

(b) Explain why the ‘spikes’ on the velocity graph are getting smaller as time increases.

(c)  Sketch the speed-time graph of the ball during this time.

Weight, mass 
and 
gravitational field strength

1.	Describe how a Newton Balance can be used to measure the size of a force.

2.	A student takes two identical pieces of paper. She crumples one into a ball and leaves the other one as a flat sheet.
	The student then drops both pieces of paper.
	Which piece of paper will land first? Explain your answer.

3.	Mass and weight mean different things.
	a.  Explain what is meant by mass.
	b.  What are the SI units of mass?
	c.  Explain what is meant by weight. 
	d.  What are the SI units of weight?

4.	Define the term gravitational field strength. 

5.	A pupil has a mass of 48 kg.
	a.  Calculate the weight of the pupil on Earth.
	b.  What would the mass of the pupil be on Mars?
c.  Calculate the weight that the pupil would be on Mars where the    gravitational field strength is 4 N/kg.

6.	A scientist predicts that a person of mass 75 kg will have a weight of
780 N on a newly-discovered planet.
    Calculate the gravitational field strength of this planet.

Friction

1.	Look at the cyclists in the picture below.

	a.  Identify three ways in which friction acting against the bicycles or cyclists has been reduced.
	b.  On other occasions, it is useful to increase the amount of friction acting.
			i.	Identify two places on a bicycle where friction is increased. 
			ii.	For each place, explain why friction should be increased.
	c.  The cyclists find that as they start off, they can accelerate easily.
After a while though, they have to pedal hard just to maintain a constant    speed.
      	Explain why this happens.

Newton’s  First  Law

1. 	a. Explain the term balanced forces.
     	b. What are balanced forces equivalent to?
     	c. State Newton’s First Law.

2. 	A weightlifter holds a bar as shown.
The mass of the bar is 180 kg.	
	a.  Calculate the weight of the bar.
	b.  What size of force did the weightlifter apply to raise the bar at a constant speed?
	c.  What is the size of force that the weightlifter applies to hold the bar stationary?

3. 	Explain, using the theory of forces, how a seat belt can prevent injury in a car crash.

Resultant Force and Newton’s 2nd Law

1.	A fully laden oil tanker of mass 6.5x107 kg sets off from its port on a bearing of 090°.
Its engine produces a force of 4.0x106N. A tugboat pushes against the tanker as shown with  a force of 3.0x106N.

090˚

180˚

270˚

000˚

4.0x106 N
Engine force

3.0x106 N
Force from tugboat

	a. Using a scale diagram or otherwise, find the resultant force acting on    the tanker.
	b. Calculate the initial acceleration of the tanker.

2.	A car of mass 1500 kg accelerates at a rate of 2.3 m/s2.
The engine of the car provides a force of 4000 N. Calculate the size of the frictional force acting on the car.

3.	A firework of mass 0.2 kg has an initial upwards thrust of 2.8 N.   
	a.  Calculate the weight of the firework.
      b.  Draw a diagram and label the forces acting on the firework.
      c.  Calculate the initial acceleration of the firework.
      d.  As the firework ascends, its acceleration increases.
      Explain why the acceleration increases.

4.	The speed-time graph for a sky-dive is shown below:

Speed (m/s)

	a.  Explain why the gradient of the graph is decreasing between 
     		0 and 20 seconds.
	b.  At what time is the parachute opened?
	c.  What is the name given to the constant velocity reached during free- fall?

Newton’s Third Law , free-fall and acceleration due to gravity

1.	Josie and Kirsty are arguing about how a water rocket water lifts off.

Dave

                       Josie                Kirsty	                                                         Dave

Dave knows that what Josie says isn’t true, but Kirsty has not provided a an    actual explanation either.

	Dave reminds Kirsty about Newton’s Third Law and they both go back
	and offer an explanation to Josie.

	Copy and complete what they say to Josie.

“OK Josie, this is to do with Newton’s Third Law, action and _ _ _ __ forces. The rocket pushes the water _ _ _ _ _ _ _, and        as a reaction, the _ _ _ _ _ pushes the rocket _ _ _ _ _ _ _      with an _ _ _ _ _ sized force. It has nothing to do with the _ _ _ _ _ pushing on  the ground. “ 
2.	Show how gravitational field strength and acceleration due to gravity are equivalent.

(Refer to your notes if you are unsure!)

3.	A student drops a football from above her head.
	It lands on the ground 0.63 seconds after being dropped.

Calculate the velocity of the ball at the instant it strikes the ground. Assume that air resistance is negligible.

4.	An astronaut drops a hammer on the Moon where the gravitational field strength is 1.6 N/kg.
	The hammer lands on the surface of the Moon 2.1 seconds after being dropped.

	a.  Show that the hammer strikes the surface of the Moon with a velocity of 3.36 m/s.
	b.  Draw a velocity-time graph for the hammer as it falls.
	c.  Use the graph to calculate the height that the hammer was dropped from.

Projectile Motion-1

Useful Equations:

where:   v is the horizontal velocity of an object (m s-1)
s is the horizontal displacement of an object (m)
t is time taken (s)

where:  a is the vertical acceleration of an object (m s-2)
v is the final vertical velocity of an object (m s-1)
u is the initial vertical velocity of an object (m s-1)
t is the time that an object accelerates for (s)

1.   Describe what is meant by ‘projectile motion’.

2.   A rock is dropped from the top of a cliff. It lands in the sea 2.7 seconds after being dropped. What is the vertical velocity of the rock when it reaches the sea?

3.   These graphs show how vertical velocity of an object changes with time. In each case,

 calculate the vertical displacement of the object.

(a)	14

(b)	11

v v / m s-1

v v / m s-1

0
t / s

1.4

0

t / s

3.8

4.   These graphs show how horizontal velocity of an object changes with time.   In each case, calculate the horizontal displacement of the object.

(a)

v H / ms

-1

3.2

(b)

5.6

v H / ms-1

0

t / s

8.0

0

t / s

0.4

5.   A monkey is relaxing in a tree when it sees a hunter climb a nearby tree and take aim with a bow and arrow. The hunter is aiming directly at the head of the monkey.

	

The monkey is smart though. It decides to jump out of the tree at the exact moment the arrow is released from the hunter’s bow.
Assume that the hunter has perfect aim, the monkey has zero reaction time and that air resistance is negligible.
Explain whether the monkey will avoid being struck by the arrow.

6.   A cowboy uses a gun to fire a bullet horizontally. He drops his gun at exactly the same time as the bullet leaves. Which will hit the ground first – the bullet, the gun or will they land at the same time? Explain your answer.
The effects of air resistance should be ignored.

7.	A high speed camera is used to analyse the motion of a ball falling with projectile motion. The ball is thrown from a height of 20 metres and photographed every 0.5  seconds as shown.

20

Vertical Distance from floor / m

16

12

8

4

0

0	3	6	9	12	15

Horizontal Distance/ m

(a) How long does it take for the ball to hit the floor?

(b) What is the horizontal velocity of the ball?

8.   A golfer hits a golf ball from the top of a hill with a horizontal velocity of 35 m s-1. The ball takes 3.0 seconds to hit the ground.

       (a) What is the horizontal displacement of the ball when it lands?

(b) What is the vertical velocity of the ball when it hits the ground?

35 m/s

9.	A plane is travelling at a constant horizontal velocity of 75 m s-1 when a box is dropped out of it. The box lands on the ground after a time of 15.5 seconds.

(a) What is the horizontal distance travelled by the box during the drop to the ground?

(b) What is the horizontal displacement of the box, relative to the plane when it hits the ground?

(c)  What is the vertical velocity of the box when it hits the ground?

(d) In reality, the vertical velocity of the box is around 55 m s-1 when it hits the ground.
Explain the difference between this value and your answer to (c).

10.	Using Newton’s Thought Experiment, explain how satellites stay in orbit around a planet.
Projectile Motion -2

1.	A javelin is launched horizontally at 5 m/s. It lands 15 metres
horizontally from its launch point.

5 m/s

15 metres

	a.  Calculate the time that the javelin is in the air for.
	b.  Calculate the final vertical velocity of the javelin.
	c.  Using a scale diagram or otherwise, find the size of the final
resultant velocity of the javelin and the angle of impact.

2.	A ball rolls off a table top with a horizontal speed of 2.0 m/s.
The ball hits the ground 0.3 seconds later.

	a.  Calculate the horizontal distance that the ball lands from the table top.
	b.  Calculate the final vertical speed of the ball.
c.  Sketch a velocity-time graph of the vertical motion of the ball. 
d.  Use the graph to find the height of the table.

3.	Explain how an artificial satellite such as the International Space Station remains in orbit around the Earth.
Energy

1.	In each of the cases below, state the main energy change involved for the vehicle.
	a.  A rollercoaster carriage rolling up a slope to a high point. 
	b.  A skier skiing down a slope.
	c.  A bus driving along a level road at a constant speed.

2.	a.  What is work done? Your answer should not be an equation!
b.  Calculate the work done by a horse when it uses a force of 800 N
		  to pull a sled a distance of 150 m.

3.	Copy and complete the table below. You must show full calculations for each problem.

	POWER(W)	WORK DONE(J)	TIME(s)	
a		400	4	
b		1000	0.5	
c	 30		10	
d	100		60	

4.	A roller coaster carriage has a mass of 300 kg when it is carrying a full load.

a.  Calculate the potential energy of the carriage when it is at the top of a drop, 30 m above the ground.
	b.  At the bottom of the drop it is at a height of 2 m above the ground.
	Calculate its potential energy now.
	c.  Calculate how much kinetic energy the carriage will have at this point.

5.	Name two quantities that affect a vehicle’s kinetic energy.

6.	A winch pulls a crate up to a height of 4 m in a time of 20 s. If the crate has a mass of 100 kg, find the power of the motor.

100 Kg

$
4 m

7.	Find the kinetic energy of a car of mass 800 kg travelling at 30 m/s.

Miscellaneous Questions - 1

l. A forklift truck is being used in a warehouse to load packing cases full   
  of electric kettles onto a waiting lorry. Each packing case has a mass of  
  48 kg.

  (a) Calculate the weight of one packing case.

  (b) The forklift truck is able to lift two cases at a time. 
        Calculate the minimum force required to lift two cases.

  (c) The forklift truck travels at a constant speed of 7 m/s across the   
       warehouse to the waiting lorry. If the total frictional force acting on 
       the truck is 500 N calculate the forward force provided by the   
       forklift truck’s engine.

2. During the summer two friends set off on a trip in a balloon. When the   
    balloon is released from its mooring it rises with a constant  
    acceleration of 0.8 m/s2. 
    The mass of the balloon and all its cargo is 360 kg.

   (a) Draw a diagram showing the forces acting on the 
         balloon at the instant it is released from its mooring.

   (b) Calculate the weight of the balloon and all its cargo.

   (c) Calculate the unbalanced force which is causing the balloon to 
        accelerate upwards.

   (d) Calculate the size of the upwards force on the balloon.
        The passengers decide to throw two sandbags overboard to help   
        them increase their height more quickly. 
        Each sandbag has a mass of 5 kg.

   (e) Calculate the new weight of the balloon and its cargo.

   (f) Assuming that the upward force stays the same as that calculated in     
        part (d) calculate the new acceleration of the balloon.

Space Exploration

For the following questions we are assessing your RESILIANCE, IMAGINATION and INGENUITY.

1/ Go onto the website www.geocaching.com/.  Choose a cache nearby to your house and write a report on what you found.

2/ Design a simple probe for entry into a planet or moon’s atmosphere.  Choose either Titan, Europa, Io or Venus.   Your report should include the following:

Any particular difficulties with your chosen moon/planet.
How it will collect information about its surroundings.
How it will send the information back to earth.
How it will slow down land safely (if at all).
How will it cope with the extreme environment (pressure, temperature, humidity etc).

Cosmology

The following questions assess your PRESENTATION skills.

1/ In less than 100 words, use your knowledge of physics and astronomy to write a History of the Universe.  You may include a diagram if you wish.

2/ Use the diagram below to identify which elements are present in the star: