Newton’s Laws Objects change velocity only when they are accelerated Acceleration happens when an object is acted on by a force The acceleration is proportional to the force, and inversely proportional to the mass (F=ma) Forces act in equal and opposite pairs The dark side of the force(s)……

A book is held stationary in place. Which of the following statements is most correct? 1. The book is stationary, there are no forces acting on the book. 2. The book exerts a downward force on my hand. 3. My hand exerts an upward force on the book. 4. The force of the book on my hand is equal and opposite to the force of my hand on the book. 5. Number 1 is false; 2,3 and 4 are all true.

Forces on a Bicycle Bicycle accelerating to the right. Wheels are turning clockwise. What is the force of the road on the bicycle? ? ?

1. To the left. 2. To the right. 3. There is no left or right force, only up. ? ?

Examples of Action-Reaction Force Pairs FORCE PAIRS are also called CONTACT FORCES.

The total force is the same. Box 1 is twice as heavy as Box 2. Does the contact force change? ? ?

Compare the contact forces in the two cases. 1. The total force is the same. By symmetry, the contact forces are the same. 2. The contact forces are higher in the top diagram. 3. The contact forces are higher in the bottom diagram.

The contact forces matter! Same force, different result! Bottom case breaks the egg, due to high contact forces.

Free body diagrams Two forces act on box 1 (neglecting friction) One force acts on box 2

What are the forces? First step: Use F=Ma for TOTAL MASS to find acceleration, a. Second step: Use F=Ma for MASS #1 to find Force on Box #1. Third step: Use “equal and opposite” to find Force on Box #2. Fourth step: Add up forces on Box #2.

Finding the forces. First step: Use F=Ma for TOTAL MASS to find acceleration, a. Second step: Use F=Ma for MASS #1 to find Force on Box #1. Third step: Use “equal and opposite” to find Force on Box #2. Fourth step: Add up forces on Box #2.

Reaction Forces & Acceleration

Compare the ACCELERATION of the Right Side boat to the Left. 1. They are equal because of “equal and opposite forces”. 2. The right boat has higher acceleration. 3. The right boat has lower acceleration.

Force of gravity. Gravity (approximately) is a constant acceleration, g, independent of mass. Therefore, the FORCE of gravity is proportional to the mass (Galileo). F gravity = -Mg F = -mg F = +mg

Tower of Babel All of the blocks have the same mass, M. They sit on top of a table. What is the total force on the stack of blocks? What is the force of the table on the stack of blocks? What are the contact forces?

What is the total force on the Tower? 1. 0Mg 2. 1Mg 3. 2Mg 4. 3Mg Each block has mass M.

What are the contact forces? 1. 1Mg, 2Mg, 3Mg 2. 3Mg, 2Mg, 1Mg 3. 2Mg, 1Mg, 0Mg 4. 0Mg, 1Mg, 2Mg F_a, F_b, and F_c are equal to: F_c F_b F_a

Problem 65: Addition of Forces When two people push in the same direction on mass m, they cause an acceleration a 1. When they push in opposite directions, the acceleration is a 2. What is the force of each person in terms of the given information? Step 1: DRAW A PICTURE! Step 2: “Givens” and “asks” Step 3: Relationships (F=ma)

Problem 65: solution M F1 F2 a1 M F1 F2 a2 How do you complete the problem? Q: Find F 1, F 2. Hint: Add and subtract the equations.

Problem 65: Given a 1 and a 2, the ratio F 2 /F 1 is: 1. a 2 /a 1 2. a 1 /a 2 3. (a 1 -a 2 )/(a 1 +a 2 ) 4. (a 1 +a 2 )/(a 1 -a 2 )

Problem 63: Hot air balloon A balloon with some passengers hovers motionless at a total mass of 1220kg. A last passenger climbs aboard, and the balloon sinks at 0.56 m/s 2. What was the mass of the last passenger? Step 1: DRAW A PICTURE! Step 2: “Givens” and “asks” Step 3: Relationships (F=ma)

Prob. 63: Setting it up. Givens: M 1 and a Asks: M p F1F1 F lift F2F2 a = m/s 2 M 1 =1220kg M 2 =M 1 +M p

Prob. 63: Solution F1F1 F lift F2F2 a = m/s 2 M 1 =1220kg M 2 =M 1 +M p Initially, acceleration is zero, so force of gravity is equal to force of lift. We know the force of gravity initially, since the mass is given. After the last passenger loads, the difference between the force of gravity F 2 and the lifting force leads to an acceleration, a.

Getting hammered? 1. Left side picture is better. 2. Right side picture is better. 3. Neither one has an advantage, the forces are the same. Which picture describes the better approach for tightening a loose hammer-head?