Physics

Newton’s Laws of Motion

Teacher: Luiz Izola

Chapter Preview

1. Force and Mass

2. Newton’s First Law of Motion

3. Newton’s Second Law of Motion

4. Newton’s Third Law of Motion

5. Forces in Two Dimensions

6. Weight

7. Normal Forces

Learning Objectives

Learn Newton’s Three Laws.

Learn How to Solve Problems related to the laws

Understanding their impact on our daily lives.

Introduction

We are all subject to Newton’s laws of motion.

Our lives are constrained and regulated by these three fundamental statements concerning matter and its motion.

Newton’s Laws are recognized as the indispensable foundation for Physics.

Force and Mass

A force is a PUSH or a PULL applied to an object. Two quantities characterize a force: magnitude and direction. Due to these two quantities, Force is considered a vector. An object’s mass is a measure of how difficult is to change its velocity. How much force must be applied to take/bring an object from/to rest. Also, how much effort is needed to change its direction. Mass is measured in Kg (kilograms).

Newton’s First Law

1. A force is required to change an object’s motion.

2. Why an object that receives a initial push, usually stops after some time?

Newton’s First Law

An object at rest remains at rest as long as no net force

acts on it.

An object moving with constant velocity continues to

move with the same speed and same direction as long

as no net force acts on it.

Newton’s First Law

Newton’s First Law is also known as the “Law of Inertia” According to Newton’s first law, being at rest and moving with constant velocity are actually equivalent. If the net force of an object is zero, its velocity is constant. (Discuss it!)

Newton’s Second Law

When you hold any object in your hand, you have to exert an upward force equivalent to the force of gravity applied on the object. If you remove your hand, the object would accelerate downward. Newton’s second law basically states that UNBALANCED FORCES CAUSE ACCELERATIONS.

Newton’s Second Law Acceleration is Proportional to Force

Newton’s Second Law

Acceleration is Inversely Proportional to Mass

Newton’s Second Law Combining these results, we find that in the simple case where with just one force in just one direction, the acceleration is given by:

Acceleration = Force / Mass

Rearranging the equation we arrive at Newton’s Second Law:

ΣF = ma

m = mass F = force a= acceleration

Because this is a vector relationship, the direction of a vector’s acceleration is the SAME as the NET FORCE acting on it.

Newton’s Second Law In terms of vectors components, we can derive the second law in terms of x, y, and z axis.

ΣFx = max ΣFy = may ΣFz = maz

If the sum of all forces acting on an object is zero, the acceleration of the object must be zero. This proves the first law of Newton. Explain

Force unit of measurement if newton (N).

Practice Session

1. In a grocery store you push a 12.5kg cart with a force of 14.0N. If the cart starts at rest, how far does it move in 3.00 seconds?

2. A 0.53Kg billiard ball is given a speed of 12m/s during a time interval of 0.04s. What force acted on the ball?

3. A baseball pitcher can accelerate a 0.15Kg ball from rest to 28 m/s in a distance of a 1.50 meters. (a) What is the average force exerted on the ball during the pitch? (b) If the mass of the ball is increased, is the force required of the pitcher increased, decreased, or the same on (a)

4. A catcher stops a 92 m/s pitch in his glove, bringing it to a rest in 0.15 meters. If the force exerted by the catcher is 803N, what is the mass of the ball?

Practice Session

5. Foamcrete is a substance designed to stop an airplane that has run off the end of a runaway, without causing injury to passengers. It is solid enough to support a car, but crumbles under the weight of a large airplane. By crumbling, it slows the plane down to a safe stop. Suppose that a 747 with a mass=1.75 x 105 Kg and an initial speed of 26.8 m/s is slowed to a stop in 122 meters. What is the magnitude of the retarding force F exerted by the Foamcrete on the plane?

Practice Session

6. A jetliner lands and begins to slow to a stop as it moves along the runaway. If its mass is 3.50x105 Kg, its speed is 27 m/s, and the net braking force is 4.30 x 105 N. (a) What is the speed 7.50 secs later? (b) How far it traveled in this time?

The Gravitational Force and Weight

All objects are attracted to earth. This attractive force is called gravitational force Fg. It is directed towards the center of the earth and its magnitude is called the weight of the object.

Fg = mass (m) x acceleration of gravity (g)

Because it depends on g, weight varies with geographic location. Objects weight less at higher altitudes

Kilogram is a unit of mass not weight.

Newton’s Third Law

“ If two objects interact, the force F12 exerted by object 1 on object 2 is equal in magnitude and opposite direction to the force F21 exerted by object 2 on object 1.”

F12 = - F21

“The action force is equal in magnitude to the reaction force and opposite in directions.”

Newton’s Laws Applications

1) A hockey puck having a mass of 0.30kg slides on the horizontal, frictionless ice surface. Two hockey sticks strike the ball at the same time, exerting the following forces on the puck:

F1 = 5.0N, north of east at 60o .(stick 1)

F2 = 8.0N, south of east at 20o. (stick 2)

Determine the magnitude and direction of the puck’s acceleration.

Newton’s Laws Applications

2) A large man and a small boy standing facing each other on frictionless ice. They put their hands together and push against each other so that they move apart. (a) Who moves away with the higher velocity? (b) Who moves farther?

Newton’s Laws Applications

3) A traffic light weighing 122N hangs from a cable T3 tied to two other cables T1 and T2 fastened to a support. T1 and T2 make angles of 37o and 53o with the horizontal. These two cables as not as strong as the vertical cable and they will break if the tension in them exceeds 100N. Will the traffic light remain hanging in this situation, or one of the cables will break?

Newton’s Laws Applications

4) A car of mass m is on an icy inclined driveway with a angle Θ with the horizontal. (a) Find the acceleration of the car assuming the driveway is frictionless. (b) Suppose the car is release from rest at the top of the incline, and the distance from the car’s front bumper to the bottom of the incline is d. How long it takes for the front bumper to reach the bottom?

Homework

1. Driving home from school one day, you spot a ball rolling out into the street. You brake for 1.20 seconds, slowing your 1.2 ton car from 80 miles/hour to 40 miles/hour. (a) What was the average force exerted on your car during the brake? (b) How far did you travel during the brake?

2. A drag racer crosses the finish line doing 212 miles/hour and prompt deploys her braking parachute. (a) What force must the chute exert on the 885 kilograms car to slow it to a 40 miles/hour in a distance of 165 meters? (b) Describe your solving strategy.

Homework3. You hold a brick at rest on your hand (a) Identify the

forces acting on the brick. (b) Is the brick in equilibrium? Explain. (c) Describe the Newton’s Law that supports your explanation.

4. On your vacation , your 1300-kg car pulls a 540-kg trailer away from a stop light with an acceleration of 1.90 meters/second2. (a) What is the net force exerted by the car on the trailer? (b) What is the net force acting on the car?

Homework

5. A force of magnitude 7.5 N pushes three boxes with masses m1 = 1.30kg, m2 = 3.20kg and m3 = 4.9kg, as shown in the picture

Homework6. A 6.0-kg block of ice resting over a table is acted on by

two forces: F1 = 13N, west of north with a 60o angle and F2 = 11N, east of north with a 30o angle. These two forces are applied by two men pushing the block of ice against the table. Think about the direction of the forces. Find (a) The ice’s acceleration. (b) the normal force exerted on it by the table.

7. A farm tractor tows a 4.3 ton trailer up a 26o incline at a steady speed of 15 miles/hour. What force does the tractor exert on the trailer? Ignore friction.

8. You pull upward a suitcase with a force of 115N, and it accelerates upward at 0.075 meters/second2. (a) What is the mass and the weight of the suitcase?

Homework9. A shopper pushes a 7.5-kg cart up a 13o incline. Find

the magnitude of the horizontal force needed to give the cart an acceleration of 1.41 meters/second2.

10. Before practicing his routine on the rings, a 67-kg gymnast hangs motionless, with one hand grasping each ring and his feet touching the ground. Both arms make a 24o angle with the vertical. (a) If the force exerted by the rings on each arm is 290N, what is the magnitude of the force exerted by the floor on his feet? (b) If the angles are greater than 24o, would the force exerted by the floor be greater than or less than the value found in (a)? Explain