Newton s Second and Third Laws and Gravity

Announcements This week: n Solutions for Quiz #1 are posted on the website: www.astro.umass.edu/~calzetti/astro100 n Homework # 1 is due on Thu, Sept. 29 th ; n Homework # 2 starts on SPARK/OWL on Thu, Sept 29 th. It is due on Friday, Oct. 7th! Next week: q Quiz #2 is going to be on Tue Oct 4 th! It is based on Units: 6,7,8,10,11,12,13,14,15,19 q EXAM 1: on Thu, Oct. 6 th!

Announcements - 2 n Tips for a successful exam: 1. Study all assigned units; use the problems at the end of each unit to test your learning. 2. Attend class; ask questions. 3. Try to do Homework # 2 before the exam. 4. Review Homework # 1. 5. Review Quiz # 1 (posted on the web) and come to Quiz # 2.

Quiz 1, Q. 9 n If you measure the angle between zenith and Polaris to be 50 degrees, you must be located at: 0 degrees latitude 50 degrees latitude 40 degrees latitude 0 degrees longitude 50 degrees longitude

Quiz 1, Q. 3 n Each day, from a point of Earth north of the equator, most stars appear to Remain stationary overhead Rise in the East and set in the West Rise in the West and set in the East Move to the North Move to the South

Today s Goals 1) To discuss Newton s Second Law 2) To introduce and discuss Newton s Third Law 3) To start introducing Newton s formulation of gravity (what keeps the Universe together!)

Assigned Reading n Second half of Unit 14 n Unit 15 n First half of Unit 16

Force To change the momentum (or motion, or state) of a body, you need a apply a force. The force needs to be a `net force : two people pushing equally against a box, but from opposite directions, will produce no change in the motion of the box. Rephrased: their net force is zero. The force can change the velocity, or the direction of motion (or both).

Vocabulary Words Speed is the distance traveled in each second it s measured in meters per second (m/s). Velocity is the speed in a particular direction it s measured in meters per second (m/s). Acceleration is the change in velocity in each second it s measured in meters per second per second (or m/s 2 )

Acceleration An acceleration is a change in velocity a = (Δ v) / (Δ t). Acceleration occurs when either the magnitude or direction of the velocity (or both) are altered. Uniform Circular Motion is Accelerated Motion How many ways can your car be accelerated?

Which of the following does NOT describe an acceleration: a car traveling with constant speed around a bend a car decreasing speed on a straight road a car traveling with constant speed on a straight road a planet traveling around a Sun

Newton s First Law (Law of Inertia) can also be stated as: In the absence of a net force, the acceleration of an object must be zero If an object is being accelerated, there must be a net force exerting on it

Newton s Second Law Acceleration is caused by force but also related to the mass of the object Force = Mass x Acceleration F = m a Or a = F/m In other words: the same force applied to a bigger (more massive) object imparts it a smaller acceleration

Survey Question Two identical spacecraft are to be accelerated by rockets. The first rocket fires with a force 4 times as great as that of the second rocket. The acceleration of the first rocket is times as great as the acceleration of the second rocket. 1) 1/4 2) 1/2 3) the same 4) 2 times 5) 4 times

There must be a force acting on the apple. What force?

There must be a force acting on the apple. What force? The force of gravity: Our own planet s `pull on all objects

The gravitational force on an object near the surface of Earth is: F grav = m g (g = 9.8m/s 2 ) Question: How do objects accelerate due to the force of gravity?

Question: Should a heavy object fall faster than a light one? Yes No

Question: Should a heavy object fall faster than a light one? Yes No The heavier object feels a larger force, but has also larger inertia!

Newton s Third Law n For every ACTION (I.e. application of a force) there is an equal and opposite REACTION (re-action) F 1 = -F 2

Newton s Third Law For any force that does not result in an acceleration, there always is an equal and opposite reaction force. Newton s third law saves us from accelerating away Box pushes down on table due to gravity. Table pushes back on box

The Third Law: F 1 = - F 2 a = F / m The lighter skater receives the largest acceleration The two skaters pushing on each other exert opposite forces

Survey Question Is the momentum (P= m v) of the two skaters conserved? Yes No Why?

Survey Question Is the momentum (P= m v) of the two skaters conserved? Yes No Why? P before = 0 P after = m 1 v 1 + m 2 v 2 = 0 P 1 =m 1 v 1 P 2 =m 2 v 2 =-m 1 v 1

Survey Question You are a shuttle astronaut returning after attempting to fix the ISS with a hammer. As you are jetting back to your shuttle, your lifeline breaks, your jets run out of fuel, your radio goes dead, and you miss the shuttle. To get back safely, you should: 1) use a swimming motion with your arms and legs 2) throw the hammer at the shuttle to get someone s attention 3) throw the hammer away from the shuttle 4) make a hammering motion in the direction of the shuttle 5) make a hammering motion away from the shuttle

What propels jets? n A jet-propelled airplane moves forward. Why? It flaps its wings, like birds The fuel gasses from the jet engines expand behind the jet and propel it forward The fuel gasses accelerate towards the back, giving a forward reaction force to the jet

Gravity n What force is responsible for motions in the universe? n What force makes objects fall? n What keeps us on the rotating Earth? n Why don t planets move in straight lines, but orbit around the Sun instead?