1.8.1 Isaac Newton - CC Physics Don Mitchell

SPH 4U Unit #1 Dynamics Topic #8: Newton’s Laws of Motion (Teacher)

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Isaac Newton(1642 – 1727)

1.8.1 Isaac Newton

In 1642, the year Galileo died, Isaac Newtonwas born in England on Christmas Day. Hisfather had died three months earlier, andbaby Isaac, very premature, was also notexpected to survive. When he was three, hismother married a wealthy elderly clergymanfrom the next village, and went to live there,leaving Isaac behind with his grandmother.The clergyman died, and Isaac's mothercame back, after eight years, bringing withher three small children. Two years later,Newton went away to the Grammar School inGrantham, where he lodged with the localapothecary (pharmacist), and was fascinatedby the chemicals. The plan was that at ageseventeen he would come home and lookafter the farm. He turned out to be a totalfailure as a farmer.

His mother's brother, a clergyman who hadbeen an undergraduate at Cambridge,persuaded Newton’s mother that it would bebetter for Newton to go to university, so in 1661 he went to Trinity College, Cambridge.Newton paid his way through college for the first three years by waiting tables andcleaning rooms for the faculty and wealthier students. In 1664, he was elected ascholar, guaranteeing four years of financial support. Unfortunately, at that time theplague was spreading across Europe, andreached Cambridge in the summer of 1665.The university closed, and Newton returnedhome, where he spent two years concen-trating on problems in mathematics andphysics. He wrote later that during this timehe first understood the theory of gravitation,and the theory of optics (he was the first torealize that white light is made up of thecolors of the rainbow), and much math-ematics, both integral and differentialcalculus and infinite series. However, hewas always reluctant to publish anything, atleast until it appeared someone else mightget credit for what he had found earlier. Trinity College, Cambridge


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Newton's first major public scientific achievementwas the invention, design and construction of areflecting telescope. He ground the mirror, builtthe tube, and even made his own tools for thejob. This was a real advance in telescopetechnology, and ensured his election tomembership in the Royal Society. The mirrorgave a sharper image than was possible with alarge lens because of chromatic aberration.

Three problems intrigued scientists in Newton'stime:

• the laws of motion, • the laws of planetary orbits, and • the mathematics of continuously varying quantities (now known as calculus).

It may be fairly stated that Newton was the first to solve all three.

1.8.2 Newton’s Three Laws of Motion

1.8.2a Newton’s First Law of Motion

Newton summarized some of Galileo’s ideas about motion to formulate the first law ofmotion. Scientists prior to Galileo thought that an object needed a net force to maintainconstant velocity. Newton’s First Law changed this thinking and is stated as:

In the absence of forces, an object at rest will stay at rest, and an object that ismoving at a constant velocity in a straight line will continue doing so indefinitely.

1.8.2a-1 Implications of Newton’s First Law

Newton’s first law is also known as the law of inertia even though it deals with bothinertia and momentum. More specifically, it predicts that:

1. An object that is stationary will remain stationary unless an external applied forcecauses it to start moving. (the principle of inertia).

2. An object that is moving uniformly will continue to do so unless an external appliedforce causes its motion to change. (the principle of momentum).


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1.8.2b Newton’s Second Law

Newton’s Second Law of Motion is most often expressed as a formula. This formularelates the acceleration of an object with the net force that acts on the object and itsmass.

(1.7)

It cannot be overstated how important this formula is to this course. A great number ofword problems can be solved using Newton’s Second Law.

Eg.#1 The V-2 military rocket, used by Germany in 1945, had a mass of about 12,000kg when loaded with fuel and 3,000 kg when empty. Its rocket engine created a thrustof 240,000 N. what was the acceleration of the V-2

a) at launch? b) at burn-out, just before it ran out of fuel?

1.8.2c Newton’s Third Law

Newton's 3rd law may be formally stated:

Forces always occur in pairs. If object A exerts a force onto object B,

then object B exerts an equal and opposite force back onto object A

or in slogan style:

Every action force has an equal and opposite reaction force

Note two important provisions: two objects must be involved and the forces act ondifferent objects!


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Planet g

Mercury 3.7 m/s2

Venus 8.8 m/s2

Moon 1.6 m/s2

Mars 3.6 m/s2

Jupiter 23.1 m/s2

Saturn 8.9 m/s2

Uranus 8.7 m/s2

Neptune 11.0 m/s2

Pluto 0.6 m/s2

1.8.2c-1 Applications of Newton’s Third Law

Some situations that Newton’s Third Law help to illustrate its usefulness:

1. When water leaves a water nozzle, the nozzle forces the water forward and the waterforces the nozzle backward. The nozzle of a big firehose has handles which firefightersmust grasp firmly, because the nozzle is forced back.

2. When jumping from a boat, your feet push back on the boat and the boat pushesforward on your feet. Before jumping from a boat to the dock, it is wise to tie the boat tothe dock first as it will move out from under you as you push on it.

3. When a bat hits a ball, the baseball forces the bat to the right (anaction) and the bat forces the ball to the left (the reaction).

Note that the nouns in the sentence describing the action force switchplaces when describing the reaction force.

1.8.3 Weight and Earth’s Gravitational Field

The weight of an object is defined as: the force exerted by the earth on that object. Wecan apply Newton’s second law of motion to determine the weight of an object on earth.Recall Newton’s Second Law:

(1.8)

The force that an object experiences due to the Earth’s gravity (i.e. its weight) is equal to its massmultiplied with the acceleration that object wouldexperience if it were released.

On Earth, any object that is released will accelerateat 9.8 m/s toward the Earth. This number is given the2

symbol “g” and is called two things:

• the “acceleration due to gravity”• the gravitational field strength

From Newton’s Second Law:

On other planets, the value of “g” differs depending on the planet as shown above.


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An interesting implication of this is that all objects will accelerate at the same rateregardless of their mass when undergoing free-fall.

Eg.#2 Two masses are attached by a thin rope and pulled by an applied force of 10.0N[right]. If the friction forces are 0.50 N[left] on the small mass and 0.70 N[left] on thelarge mass,

a) find the net force acting on the system of masses

b) find the acceleration of the masses. c) find the tension in the middle rope.


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Eg.#3 Two masses are shown attached to a massless rope suspended overa frictionless pulley.

a) Determine the magnitude and direction of the acceleration of each mass.

Taking clockwise rotation of the pulley to be positive:

1 24.0 kg. mass (m ) 4.5 kg. mass (m )

Setting these equal to one another, we obtain:

The 4.0 kg. block accelerates at 0.58m/s [up] and the 4.5 kg. block accelerates at2

0.58m/s [down].2

b) Determine the tension in the rope.

It is sufficient to find the magnitude of thetension force which we can do by evaluating either of the expressions for tension above:


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Eg.#4 Two masses are shown attached to amassless rope suspended over a frictionlesspulley on a frictionless ramp.

a) Determine the magnitude and direction ofthe acceleration of each mass.

Taking clockwise rotation of the pulley aspositive:

1 24.5 kg. mass (m ) 3.0kg. mass (m )

Setting these two expressions equal,

The 4.5 kg. mass accelerates up the ramp at 0.55m/s and the 3.0 kg mass accelerates2

downward at 0.55m/s .2

b) Determine the tension in the rope.

Once again, determining the magnitude of the tension is sufficient.


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Worksheet #1.8

1. You apply a force of 0.35N.[up] to lift a fork. The resulting acceleration of the fork is0.15m./s. [up]. Determine the mass of the fork.2

2. A hot air balloon experiences an acceleration of 1.10 m./s. [down]. The total mass of2

the balloon, basket and contents is 315 kg.

a) What is the upward buoyant force on the system?


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b) The balloonist wants to change the acceleration to zero. There is no fuel left to heatthe air in the balloon. Determine the mass of the ballast that must be discardedoverboard. (Neglect air resistance).

Therefore 35 kg. must be discarded

3. A tree house has a vertical “fire pole” of smooth metal, designed for quick exits. Achild of mass 35.7 kg. slides down the pole with constant acceleration, starting fromrest. The pole is 3.10m. high and the journey to the ground takes 2.00 seconds.

a) What is the acceleration of the child? b) What is the force of friction exerted by the pole onto the child?


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4. When an external net force is applied to a particular mass “m”, an acceleration ofmagnitude “a” results. When the mass is increased by 2.0 kg. and the same net force isapplied, the acceleration is 0.37a. Determine the mass m.

5. A boy pushes a lawnmower (m = 17.9kg.) starting from rest acrossa horizontal lawn by applying a force of 32.9 N. directly along thehandle, which is inclined at an angle of 35.1 degrees below thehorizontal. The lawnmower accelerates at 1.37m./s. for 0.58 s. after2

which the mower moves at a constant velocity. Determine:

a) The normal force on the mower

Mr. Spencer

Arrow

Mr. Spencer

Pencil

Mr. Spencer

Pencil


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b) The force of friction on the mower. c) The maximum velocity of the mower.

d) The force supplied by the boy in order to keep the mower moving at the samevelocity.


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6. Blocks A and B are connected by a string thatpasses over a frictionless pulley as shown below.When the blocks are moving, block A experiences a

A Bfriction force of 5.7N.[back]. If m =2.7kg. and m =3.7kg. calculate:

a) The acceleration of the blockschoosing CW rotation of the pulley as the positive direction:

b) The tension in the string.

Mr. Spencer

Arrow

1.8.1 Isaac Newton - CC Physics Don Mitchell

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