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4 | Newton's Laws of Motion ENGAGE: Spinning eggs Have you ever hardboiled an egg and put it back in the refrigerator with the

other eggs only to forget which one is hard boiled? Apart from cracking them

open until you find the hard one, how can you figure out which egg you want?Try spinning them ona lat surface.

1. (a) What happens to the movement of the boiled egg if you gently stop it spinning with your finger?

(b) What happens to the movement of the raw egg if you gently stop it spinningwith your finger?

(c) Suggest a reason for the observations you saw:.

EXPLORE: A thought experiment Have you heard of the expression "a thought experiment"? Albert Einstein was well known for his use of thought experiments to illustrate concepts that follow a pattern of logic, but are virtually impossible to show practically.

Galileo was also wel-known for using thought experiments. One of his most important ones was to demonstrate what would eventually happen to a ball rolled down the ramp if there was no friction at the bottom.

He started by rolling a ball on ramps which had equal height and angle (below). The ball never quite reached the top of the second ramp because of friction. Galileo reasoned that if there was no friction, the ball would reach the

top of the second ramp.

Decreasing the angle of the second ramp would result in the ball taking a longer route to the top of the ramp:

2. (a) Complete the diagram to show the forces acting on the bal at point A and B in the diagram (assuming no friction):

A B

(b) Predict what would happen to the ball if the second ramp was laid out flat:

6 Galileo reasoned that if the second ramp was laid flat, then in a frictionless situation the bal would keep rolling.

3. (a) What force causes the ball to gain speed as it rolls down the first ramp?

(b) What foroce causes the ball to lose speed as it rolls up the second ramp?

(c) Is there any unbalanced force acting on the bail while on the flat surface?

(d) Why would the ball continue to roll forever if the second ramp was laid flat?

() Try writing your explanation as a simple rule of motion: .

EXPLORE: Force, mass, and acceleration

You have seen earlier that weight is the effect of the acceleration of gravity on an object. By using string and a pulley, the force of gravity accelerating a falling object can be used to accelerate a trolley horizontally along a bench at the same time.

Two students were investigating acceleration. If they keep the force constant, they wondered what effect changing the mass would have on the acceleration:

Load

-Loaded trolley Bench Pulley

Timer tape Ticker timer

1 kg- The mass at the bottom of the string was kept at 1.0 kg during the experiment so that the accelerating force stayed constant at 9.8 N. The mass of the trolley plus its load was progressively increased for each trial as follows: 0.5 kg> 0.7 kg > 0.9 kg > 1.1 kg 1.3 kg 1.5 kg.

The corresponding increase in the total mass of the systenm (loaded trolley mass + 1 kg) for each trial is therefore 1.5 kg1.7 kg > 1.9 kg 2.1 kg2.3 kg 2.5 kg.

Before the 1 kg mass was attached to the string, they compensated for friction by squeezing a suitably sized pieceof plasticine onto the string, just below the pulley. If the system (loaded trolley, pulley, string, and ticker tape with timer running) moves at near constant speed after being given a slight nudge then, as near as possible, frictionwithin the system has been balanced out.

They attached timer tape to the trolley and threaded the tape through a ticker timer.

They then started the timer and let the trolley go. The trolley rolled forward as the 1 kg fell to the floor. When it hit the floor, they stopped the ticker timer.

The students reset the equipment and repeated the procedure to produce a tape for each different total mass.

By counting the spaces between the dots on the timer tape the students were able to calculate the exact time the 1 kg was falling. Each space is equal to 0.02 seconds (the timer makes 50 dots per second). They multiplied the number of spaces by 0.02 to determine the exact time the 1 kg was falling.

The distance the trolley rolled was determined by measuring the distance between the first and last dot.

Their results are shown in the table on the following page:

4. Explain the physics behind the technique used to compensate for friction:

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Acceleration System mass (kg)

Force causing Total time DistanceTrial

System mass acceleration (N) (s) (m) (m/s)

9.8 0.61 1.2 1 1.5

2 1.7 9.8 0.64 1.2

3 1.9 9.8 0.68 1.2

2.1 9.8 0.72 1.2

5 2.3 9.8 0.75 1.2

2.5 9.8 0.78 1.2

5. (a) Complete the column for the 1/system mass during each trial

(6) Complete the acceleration column using the equation a = 2d to calculate the acceleration of the trolley:

(c) Plot acceleration vs 1/system mass with a line of best fit below. We use 1/system mass so the slope is positive:

NEED HELP? See activity 58

- -H--HHHEH4-

-

--

- i - t - - t H-i

--+-F

.L- J- - -t ---- -* HiFE

- 4- - t- -11- 1 +

- i- - -- - "

-

-- - - -- - t- - - - ++ t

-

1LiJ LL.i L - - -- -f- FH- -+-- -

4-

i - HI-T4-

L. . 14- 1 -1 -- - 4.t.--}- -1- : --+ it:r:

LiLLL 4 - i- -L - r - - 1

T .1

6. (a) What was the general effect on the acceleration when more mass was added to the system?

(b) Calculate the gradient of the graph:.

(c)The graph is a straight line, so it has the equation a = gradient x 1/m intercept. From F = mxawe have the equation a = Fx 1/m +0.By comparing these two equations what is the value of F? Comment on its significance.

A second group of students used the same equipment to carry out a slightly different investigation. They wanted to keep the mass of the system constant while increasing the force acting on the system. They achieved this by moving masses from the loaded trolley and adding them to the 1 kg at the bottom of the string

Their results are shown in the tablebelow

Force causing the

acceleration (N) Acceleration System mass

(kg) Mass causing the acceleration (kg) Trial Total time (s) Distance (m)

(m/s)

2.6 1.0 0.70 1.2

2.6 1.2 0.67 1.2 2

2.6 1.4 0.65 1.2

2.6 1.6 0.63 1.2

2.6 1.8 0.62 1.2 5 6 2.6 2.0 0.60 1.2

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7. For the table at the bottom of the previous page:

(a) Complete the column for the force causing the acceleration during each trial (in newtons).

(b) Complete the column for the acceleration during each trial using the equation a = 2d +

(c) Plot a graph of acceleration versus force, with a line of best fit, on the grid below:

-

--

-H-

-

- --

4- 4- - - -

8. What was the general effect on the acceleration when more force was used?

9. (a) Calculate the gradient of the graph:.

(6) The graph is a straightline, so it has the equation a = gradient x F + intercept. From F= mx a we have the equation a = 1/m x F + 0. By comparing these two equations, calculate a value for m. Comment on its significance:

EXPLAIN: Free body diagramns

Free body diagramsare used to show the forces acting upon an object. They do not show the reaction forces of the object upon its environment. Consider the photograph of the jet fighter in level flightbelow

FLit

Drag

hrus

g (weight)

This free body diagram shows the forces acting on the jet.If it is flying horizontally at constant velocity, then the forces will be balanced. The force due to gravity acting on the aircraft is balanced by lift force generated by the wings. The thrust force of the engine is balanced by the drag force caused by air resistance.

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The diagrams below show the forces acting on the trolley of 0.5 kg at different times:

Box 1 Box 2 Box 3

Fa (normal tforce) F (normal force) F (normal force)

Friction 1 N Thrust 5 N Friction 1 N Thrust 1 N Friction 1 N Thrust 0 N

Fg

10. (a) Complete the table below:

Box 1 Box 2 Box 3

F(net) (net) (net)

m m m

a a

(b) Describe the motion of the trolley in box 1:

(c) Describe the motion of the trolley in box 2:,

(d) Describe the motion of the trolley in box 3:

11.The battery in Rebekah's car has gone flat. Michael and Eddy are push-starting the car. The diagram below shows the forces applied to the car. The men need to apply enough foroe to overcome the forces opposing the movement of the car. The mass of the car is 910 kg.

Eddy 400 N

Michael 450 N

O.

Internal friction 530 N

Friction with road 150 N

Draw a free body diagram showing the net forces applying to the car:

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EXPLAIN: Acceleration and force 12. The graph below shows the velocity of a medium sized passenger plane as it accelerates down a runway and lifts off.

The plane has a mass of 70,535 kg: Velocity of alrcraft

100.0 90.0 80.0 70.0 60.0 50.0

40.0 30.0 20.0

10.0 0.0

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0

Time (s)

(a) What was the acceleration of the plane between 10 seconds and 30 seconds?

(b) Assuming there is no friction on the runway, what was the force of the thrust produced by the engines?

(c) In reality, there is friction between the plane's tires and the runway. Use this to explain why the acceleration of the plane suddenly increases at the 35 second mark:

(d) What distance did the plane cover between 6 seconds and 35 seconds?,

13. The graphs below show the velocity of various high performance vehicles:

Velocity of high performance vehicles

160.0T

140.0

120.0E 100.0 Top fuel dragster

Indycar80.0t Formula 1 car

60.0+ Subaru Imprezza WRX

40.0 Lamborghini Diablo

20.0

0.0 0.0 1.0 20 3.0 4.0 5.0 60 7.o 80 9o 10.0

Time (s)

(a) Calculate the acceleration of the top fuel dragster:

(b) Given that the dragster has a mass of about 1050 kg, what force does the engine produce?

(c) Why would your answer for (b) be an underestimate of the force provided by the engines?

----------..-..-----.--.------- ---------

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lon thrusters are a type of spacecraft propulsion system. Unlike chemical rockets, which burn large amounts of fuel to create enormous thrust, ion thrusters accelerate ions through an electrical field, creating very litte thrust. However because they use the ion "fuel" slowly the thruster can remain active for very long lengths of time.

NSTAR ion thruster lon thruster. on the Deep Space

spacecraft

The Dawn spacecraft was launched in 2007 and arrived at Ceres in 2015. Its

main propulsion systems was a xenon

based ion thruster.

14. lon thrusters produce only small amounts of thrust. The mass of the dawn spacecraft was 1.2177 x 10 kg. It took 96 hours to accelerate from 0 to 96 kilometers per hour. Calculate the force of the ion thruster produced:

EXPLORE: Action reaction The picture of the near right shows the space shuttle Endeavour on the launch pad, before launch. What are the forces acting on the stationary shuttle? The shuttle presses down onto the Earth because launch pad for simplicity). But the shuttle isn't going down

through the ground. Something is stopping it. What?

gravity (we'll ignore the

Forces come in pairs. The force of the shuttle pressingdown on the Earth is balanced by the reaction force of the Earth pressing back against the shuttle. These forces are always equal and opposite.

15. Draw arrows showing the two forces mentioned above onto the photo of the space shuttle. Label them Fs (for force of shuttle on Earth) and FEs (for force of Earth on shuttle).

16. At launch, the shuttle's engines provide a force (thrust) to lift the shuttle off the launchpad. What forces are acting on the shuttle now? Draw arrows on the photo to show the forces on

the shuttle. Label the forces appropriately.

17.(a) The image below shows a ferry being driven forward. The engines are providing the action force (thrust). The hull provides another action force (buoyancy). On the photo, draw and label the action and reaction forces on the ferry.

usAND

(b) Describe how the action and reaction forces act on the ferry:

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Recall the free body diagram of the fighter jet on page 18. Are the forces shown (lift/weight and thrust/drag) action reaction "force pairs"? Because they are acting on the same object (the aircraft) they are not. The diagram below shows the force-pairs acting on the aircraft.

alraraft-Earth Falirwings (it) aircraft-air air-aircraft(drag)

exhaust-aircrafit thrust

aircraft-exhaust Earth-airoraft (Weight

wings-air

18. (a) If the aireraft increases its altitude, what are the main forces involved and explain what needs to happen to them:

(b) In the left box below show the force pairs operating as the aircraft gains altitude and in the right box below show the free body forces operating as the aircraft gains altitude:

Force-pairs Free body diagram

19. (a) Form small groups and use at least two reference sources to research one of the laws of motion identified below. Make a visual presentation to the class to include a general description of the law and an example demonstrating application of the principle.

(b) Using what you have leaned in this activity and from the presentations of your classmates, describe an example of each of Newton's three laws below.

Law Description Example

First law: Law of inertia

Every object in a state of uniform motion tends to remain in that state of motion unless it is subjected to an unbalanced external force.

(a)

Second law:

Definition of force F (b) ma

An object's acceleration (a) depends on its mass (m) and the applied force (F).

For every action, there is an opposite and equal reaction. When one body exerts a force on a second body, the

second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

Third law: (c) Law of reciprocity