Chapter 5: Newton's Laws of Motion

“If I’ve seen further than others, it is because I have been standing on the shoulders of giants”

• Born December 25, 1642.• Rather solitary• Known for strange inventions and

inclination for mechanical works like windmills, kites, four-wheeled vehicles run by cranks, sundials, etc.

• Sent out to look after sheep, spent time building waterwheels, dams, etc. leaving sheep to run wild.

• 1661 set out for Cambridge. He spent sleepless nights and days without eating in pursuit of his investigations.

• 1665 the Plague arrived. It was dangerous to stay in the cities. He left.

• The leisure afforded by that time permitted him to explore physics and mathematics. He spent many years developing his ideas before publishing them

• He “invented” physics and calculus. He also studied religion and alchemy.

Chapter 5: Newton's Laws of Motion

“If I’ve seen further than others, it is because I have been standing on the shoulders of giants”

• He published “Principia” in Latin in 1687• He refined and republished in 1713 and

1726.• It contained his 3 laws of motion, his law

of universal gravitation, and a derivation of Kepler’s 3 laws of planetary motion.

Newton’s First Law of Motion

Inertia

An object continues in a state of rest, or of motion in a straight line at constant speed, unless it is compelled to change that state by forces exerted upon it.

(Def: A force is a push or a pull)

If Σ f = 0 then a = 0

A force is a push or a pull.Forces are vectors (and add as vectors).Forces produce accelerations.

Newton's Second Law of MotionForce = mass * acceleration

Σ F = ma

How much force is needed to cause a 2 kilogram mass to accelerate at 3 m/s2 ?

Σ F = ma = 2 kg * 3 m/s2 = 6 kg m/s2

1 kg m/s2 is defined as a Newton (abbreviated N)Therefore the answer is 6 N

Mass -A Measure of the inertia of an object. It is measured in kilograms.

Mass vs. VolumeInertia vs Space occupied.

Mass vs. WeightInertia vs Force of Gravity on an object.

Mass vs. WeightInertia vs Force of Gravity on an object

The force of gravity is proportional to the mass but the proportionality constant depends upon the location.

Relative Gravities

Mercury- .378Venus- .907Earth - 1Mars- .377Jupiter- 2.364Saturn- .916Uranus- .889Neptune- 1.125Pluto (not a planet)- .067Moon- .166Sun- 27.551

In space the rock has no weight but it still has the same inertia!

Question: What is the weight of 1 kilogram on the earth?

Weight is the force of gravity on an object. Therefore, weight = (mass) * (acceleration of gravity).On earth, the acceleration of gravity is 9.81 m/s2

Therefore, since Σ F = maF = (1 kg)*(9.81 m/s2 ) = 9.81 N

You do not have to know this, but 1 kilogram weighs about 2.2 pounds.

Silly question: Which weighs more a pound of lead or a pound of feathers?

1. Would a 2 kilogram piece of lead havea. twice as much mass as a 1kilogram piece of lead?b. twice as much inertia at a 1 kilogram piece of lead?c. twice as much weight as a 1 kilogram piece of lead (assuming they were weighed at the same location)d. twice as much volume as a 1 kilogram piece of lead?

2. Compare 2 kilograms of bananas to 2 kilograms of breada. in terms of how much Mass is each hasb. in terms of how much inertia each hasc. in terms of how much volume each hasd. in terms of how much weight each has

What happens when you lift the sledgehammer?What happens when you stop lifting the sledgehammer?What happens when you bring it down?

Explain in terms of weight AND ALSO in terms of mass.

Mass is a measure of the inertia of an object. (Therefore more mass, less acceleration).

A 57 kg boy is pulling a 4.6 kg sled. He is applying a force of 6.2 N at an angle of 35 degreesAbove the horizontal. Assuming the sled starts at rest and friction with the ice is negligible,Calculate the speed of the sled after 1.15 seconds.

A 57 kg boy is pulling a 4.6 kg sled. He is applying a force of 6.2 N at an angle of 35 degreesAbove the horizontal. Assuming the sled starts at rest and friction with the ice is negligible,Calculate the speed of the sled after 1.15 seconds.

(A) First calculate the acceleration. A=f/m. However, the sled will accelerate horizontally, so only the horizontal component of the force is of interest so you must calculate the horizontal component of the force and use that to get the acceleration.

(B) Then use the acceleration formula to find the final speed.

The answer is 1.27 m/s

For every force or action, there is an equal but opposite forceor reaction. The action and reaction act on different objects.

-----------------------Action = Reaction-----------------------

I stand on the ground.The force which I exert on the ground is equal and opposite in direction to the force the ground exerts on me.I push down on the ground. The ground pushes up on me.

Newton's Third Law of Motion:

The cannon just fired a ball.Which of the following is true?a) The force the cannon exerted on the ball was larger than the force the ball exerted on the cannon.b) The force the ball exerted on the cannon was larger than the force the cannon exerted on the ball.c) The force the cannon exerted on the ball was the same size as the force the ball exerted on the cannon.

1. What is the weight of 2 kilograms of iron?Forces of 10 N and 4 N act in opposite directions. What is the magnitude of the resultant force?2. What is the weight of a 2.5 kilogram object (in Newtons)?3. In the cabin of a jetliner that cruises at 600 km/hr, a pillow drops from an overhead rack into your lap below. Since the jetliner is moving so fast, why doesn't the pillow slam into the rear of the compartment when it drops?

2 kilogram mass

2 N downward force applied here

What is the tension here?

Friction:

Questions:What is the effect of friction on a moving object?The speed of a ball increases as it rolls down an incline and it decreases as it rolls up an incline. What happens to the speed if it rolls on a horizontal surface?Inertia says that no force is required to maintain motion. Why, then, do you have to keep pedaling your bicycle to maintain motion?A space probe was launched toward Jupiter. How much force is necessary to keep it moving once it is far from Earth’s gravity?

Static - fixed or stationary - not moving

Kinetic - moving

FRICTIONFriction is a force which opposes the motion of one surface over another.

- Often it is undesirable (uses up gasoline, causes wear, etc.)

- Often it is useful (you need friction to walk and to stop)

REAL IMPORTANT DEFINITION:

Normal - a line drawn perpendicular to the surface

Force of static friction < = coefficient * Normal force

F <= μs N

F = μk N

Force of kinetic friction = coefficient * Normal force

=D/B

A football lineman often attempts to get his body under that of his opponent and push upward. Why?

What effect does this have on the friction force between the opposing lineman's feet on the ground?

Rule 0:If there is no mention of friction it us usually safe to assume that there is no friction acting in the problem. If the question mentions friction, or asks about it, you need to be more careful. Rule 1:If an object is moving at constant velocity, or constant speed in a straight line, that means that the acceleration is zero and the sum of the forces acting is zero. If you know that some force is acting, then there must be another force (usually friction) which is acting in the opposite direction to make the sum of the forces equal to zero.Rule 2:If an unbalanced force is acting, then it must cause an acceleration which is given by a=F/m.

Summary Rules for Newtons Laws

Newton’s Laws problems with friction1. A force of 35 N acts to the right on a 10.0 kilogram mass causing the mass to

accelerate at 2.7 m/s2 . What is the magnitude and direction of the force of friction?

2. An elevator has mass of 250 kilograms when empty. A person having mass 75 kilograms is inside it. (A) What tension in the cable is necessary in order to cause the elevator to accelerate upward at 1.5 m/s2? (B)Assume the elevator cable snaps. How much friction must be supplied by the brakes in order for the elevator to remain stationary? (C) How much friction would it take to let it move downward at a constant velocity?

3. Your weight is 700 N. You are standing on a spring scale inside an elevator. (A) What will the scale read if the elevator is not moving? (B) What will the scale read if the elevator is accelerating upward at 2.0 m/s2 ? (C) What will the scale read if the elevator is accelerating downward at 2.0 m/s2 ? (D) What will the scale read if the elevator is moving UPWARD at a constant 2 m/s? (E) What will the scale read if the elevator is moving down at a constant 2 m/s?

Text page 184 # 104Wilbur is asking Mr. Ed the talking horse to pull a cart. Mr. Ed replies that he would like to, but the laws of nature just won’t allow it. According to Newton’s third law, he says, if he pulls on the cart, it pulls back on him with an equal force. Clearly, then, the net force is zero, and the cart will stay put. How should Wilbur answer the clever horse?

Newton’s Laws Problems1. What is the weight of a 2.3 kg mass?2. You push a 12.3 kg shopping cart with a force of 10.1 N. (a) What is the acceleration of the cart? (b) If the cart starts from rest, how far does it move in 2.50 seconds?3. What net force must act on a 540 kg golf cart to give it an acceleration of 2.5 m/s2 ?4. The net force acting on a backpack is 23 N. If the acceleration of the backpack is 3.8 m/s2 what is its mass?5. A 1800 kg truck pulls a 620 kg trailer away from a stoplight with an acceleration of 1.16 m/s2 . What is the net force acting on the trailer? On the truck?6. Responding to an alarm a 782 N firefighter slides down a pole to the ground floor 3.3 m below. The firefighter starts at rest and lands with a speed of 4.2 m/s. Find the average force exerted on the firefighter by the pole.7. (This looks hard because there are no numbers!) When two people push in the same direction on an object of mass m, they cause an acceleration of magnitude a1. When the same people push on the object in opposite directions, the acceleration of the object has the magnitude a2. Determine the magnitude of the force exerted by each of the two people in terms of m,a1, and a2.8. A girl slides down a rope. As she slides faster and faster, she tightens her grip, increasing the force exerted on her by the rope. What happens when this force is equal in magnitude to her weight? Explain.9. A person has a mass of 80 kilograms. What is that person’s weight (in Newtons?)10. A person pulls a cart by applying a 10.0 N force at an angle of 30 degrees above the horizontal. Assuming there is no friction, calculate the acceleration of the cart, assuming the cart has a weight of 35 N.

Newton’s Laws Problems (Continued)

11. A person whose mass is 75 kilograms is standing on a scale calibrated in Newtons. What will the scale read if he is at rest?

12. Now assume the person is in an elevator which is accelerating up at 2.0 m/s2 . What will the scale read?

13. Now assume the elevator is accelerating down at 3 m/s2 . What will the scale read?

14. Now assume the elevator is moving up at a constant speed of 2 m/s. What will the scale read?

15. Now assume the elevator is moving down at a constant speed of 3 m/s. What will the scale read?

16 A boy of mass 75 kilograms is in an elevator of mass 580 kilograms. The elevator is supported by a cable which runs up to a motor. What force must the cable supply in order to accelerate the elevator and its occupant upward at 2.5 m/s2 ?

17 A 15 N force acts toward the right 30 degrees above the horizontal on an 8 kg mass. A frictional force of 6.0 N also acts on the mass. Find the magnitude of the acceleration of the mass.

ANSWERS Newton’s Laws Problems

1. 22.6 N2. (A) 0.821 m/s2 (B) 2.57 m3. 1350 N4. 6.05 kg5. Trailer = 719 N Truck = 2088 N6. 569 N7. F1 = m(a1+a2)/2 F2 = m(a1-a2)/28. She continues at constant velocity9. 785 N10. 2.4 m/s2

11. 736 N12. 886 N13. 511 N14. 736 N15. 736 N16. 8063 N 17. 0.87 m/s2 .