Newton's Second Law

Forces are Unbalanced

There is an acceleration

The acceleration depends

Directly upon the

〝 net force〞

The acceleration depends

inversely upon the

〝 object mass〞

Newton's Second Law

• The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

This verbal statement can be expressed in equation form as follows: a = Fnet / mThe net force is equated to the product of the mass times the acceleration. Fnet = m × a

• The acceleration of an object increases with increased force, decreases with increased mass, and is in the same direction as the force.

Sampe Problem

• What force is needed to accelerate a 10kg shopping

cart 3 m/s2?

• If a 5 kg ball is accelerating 1.2 m/s2, what is the

force on it ?

• A person on a scooter is accelerating 2 m/s2. If the

person has a mass of 50 kg, how much force is acting

on that person?

Sampe Problem

• If a team pulls with a combined force of 9000N on an airplane with a mass of 30000 kg, What is the acceleration of the airplane?

• Half the people on the team decide not to pull the airplane. The combined force of those left is 4500N, While the airplane’s mass is still 30000 kg. What will be the acceleration?

• A girl pulls a wheeled backpack with a force of 3N. If the backpack has a mass of 6 kg. What is its acceleration?

Sampe Problem

• A model rocket is accelerating at 2 m/s2. The force on

it is 1N. What is the mass of the rocket?

• Another model rocket is accelerating at a rate of 3

m/s2 with a force of 1N. What is the mass of the

rocket?

• A boy pushes a shopping cart with a force of 10N,

and the cart accelerates 1 m/s2. What is the mass of

the cart?

【 Example】1. Determine the accelerations that result when a

12-N net force is applied to a 3-kg object and then to a 6-kg object.

A 3-kg object experiences an acceleration of 4 m/s2.

A 6-kg object experiences an acceleration of 2 m/s2.

【 Example】2. A net force of 15 N is exerted on an encyclopedia to

cause it to accelerate at a rate of 5 m/s2. Determine the mass of the encyclopedia.

Use Fnet= m * a with Fnet = 15 N and a = 5 m/s2.

So (15 N) = (m)*(5 m/s2)

And m = 3.0 kg

【 Example】3. Suppose that a sled is accelerating at a rate of 2 m/s2.

If the net force is tripled and the mass is doubled, then what is the new acceleration of the sled?

Answer: 3 m/s2

The original value of 2 m/s/s must be multiplied by 3 (since a and F are directly proportional) and divided by 2 (since a and m are inversely proportional)

【 Example】• An applied force of 50 N is used to accelerate an

object to the right across a frictional surface. The object encounters 10 N of friction. Use the diagram to determine the normal force, the net force, the mass, and the acceleration of the object. (Neglect air resistance.)

Newton's third law

Forces act in pairs.

1. Newton's third law relates action and reaction forces.The key points to Newton“s third law are that when

objects A and B interact ，the force of A on B equals the force of B on A; and

the forces are opposite in direction.

In action/reaction pairs either force can be considered the action force or the reaction force.The two forces occur simultaneously ．

• Example ： When you push down on a table ， the force from the table's resistance increases instantly to match your force.

Action/reaction force pairs occur when any two objects interact, not just through contact forces.

• Example ： The pull of Earth on a falling baseball is exactly that of the baseball on Earth.Earth is so much more massive,however,that Earth's acceleration from the pull is nearly nothing.The acceleration of the baseball is quite noticeable ．

2.Newton's three laws describe and predict motion

• Newton‘s laws work together to explain changes in the motion of objects,such as a squid moving forward when squirting water backward,or a bird flying higher or changing direction.

• Newton's laws are also useful in calculating how objects move under the conditions found in everyday life.Scientists such as Albert Einstein have added to our understanding of motion since Newton's time.Under certain conditions, such as extreme speed or extreme gravity,Newton's laws need to be adjusted.

Newton's Third Law

• For every action, there is an equal and

opposite reaction.

The statement means that in every interaction, there is a

pair of forces acting on the two interacting objects. The

size of the forces on the first object equals the size of the

force on the second object. The direction of the force on

the first object is opposite to the direction of the force

on the second object. Forces always come in pairs - equal

and opposite action-reaction force pairs.

Consider the flying motion of birds.

• A bird flies by use of its wings.

• The wings of a bird push air downwards. Since forces result from mutual interactions, the air must also be pushing the bird upwards.

• ：地球對書本的吸引力 ,

• ：書本對地球的吸引力。

• 且為作用力與反作用力。

1. Who was the scientist who gave us the Laws of Motion?

2. How many Laws of Motion are there?

3. What is another name for the first law of motion?

4. Which law explains why we need to wear seatbelts?

5. Which law says that force is equal to mass times acceleration (F=MA)?

6. Which law says that heavier objects require more force than lighter objects to move or accelerate them?

7. Which law explains how rockets are launched into space?

8. Which law says that for every action there is an equal and opposite reaction?

• 1. Who was the scientist who gave us the Laws of Motion?

• Answer: Sir Isaac Newton

2. How many Laws of Motion are there? • Answer: three

3. What is another name for the first law of motion?

• Answer: Law of Inertia

4. Which law explains why we need to wear seat belts?

• Answer: First Law of Motion

5. Which law says that force is equal to mass times acceleration (F=MA)?

• Answer: Second Law of Motion

6. Which law says that heavier objects require more force than lighter objects to move or accelerate them?

• Answer: Second Law of Motion

7. Which law explains how rockets are launched into space?

• Answer: Third Law of Motion

8. Which law says that for every action there is an equal and opposite reaction?

• Answer: Third Law of Motion

Forces can change the direction of motion.

• Force can change the direction of an object without changing its speed if the force acts at right angles to the motion.

• A force that continuously acts at right angles to an object's motion will pull the object into circular motion.

• Any force that keeps an object moving in a circle at a constant speed is called a centripetal force.

• The centripetal force needed to keep an object moving in a circle depends on the mass of the object, the speed of the object,and the radius of the circle.

• Centripetal force radius

speedmass 2‧