Physics 218 Alexei Safonov Lecture 6: Dynamics

Boat on the River You want to cross the river so that the boat gets exactly from A to B. The river has a current v C =4 km/h. Your boat’s speed in still water is v B =20km/h? What is the angle  you should aim at to do that?  vBvB

In previous problem, is it possible to get from A to B for any values for v B and v C ? A.Yes, always possible B.Only possible if v B >v C C.Only possible if v B >2v C D.Only possible if v B >>v C (much larger)  vBvB vCvC

Earth rotates, which means we are rotating with it. How big is the acceleration due to Earth's rotation acting on us?

R=3,959 miles T=24 hrs V equator = 2  R/T

Rescue Plane You are the pilot of a rescue plane. Your mission is to drop supplies to isolated mountain climbers on a rocky ridge a height h below. If your plane is traveling horizontally with a speed of V O : How far in advance of the recipients (horizontal distance) must the goods be dropped?

Overview of Chapter 4 Where we’re going and why –Dynamics vs. Kinematics Force Newton’s Laws of Motion Mass Normal Force Example problems –Note: It’s important to be good at 2- Dimensional motion at this point

Where we’re going and why Moving from: “How things move” Kinematics To: “Why things move that way” Dynamics Why do you care? Different questions: –Old: What acceleration do you need to go from 0 to 60mi/hr in 6 sec? –New: How much force does your car engine need to exert? Use all the kinematics, vectors and calculus from Chapters 1-3 Plan: Do the concepts, then do the problems

You shouldn’t memorize them, rather you need to be able to understand and use them Don’t write them down from the overheads, they’re in your book. We’re going to translate them into English Big picture: Force Newton’s Laws

Force: Our First Concept What is a Force? Examples: –Push –Pull –Slap –Gravity –Others?

Newton’s First Law “Every body continues in it’s state of rest or of uniform speed in a straight line unless acted on by a non- zero net force”

Translate that into English: Force To cause an acceleration (change the velocity) requires a Net Force or If there is an acceleration, there must be a net Force Force is a Vector Add up all the forces (vectors) to find the Net (or total) force

Newton’s First Law Example of non-zero net forces: –Friction: Makes a moving block slow down –Gravity: Makes a ball fall toward the earth Example of zero net force –Car just sitting on the pavement No velocity, no acceleration→ no net force –Rocket ship in outer space Nothing to slow it down → constant velocity →no net force

Newton’s Second Law “The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force action on the object”

Translate: Newton’s Second Law The acceleration is in the SAME direction as the NET FORCE  This is a VECTOR equation  If I have a force, what is my acceleration?  More force → more acceleration  More mass → less acceleration

Acceleration is caused by force. A bigger mass requires more force to achieve the same acceleration Newton’s 2 nd Law

If an object is moving with acceleration, then the net force acting on it is not zero. A.True B.False

CheckPoint The net force on a box is in the positive x direction. Which of the following statements best describes the motion of the box : A) Its velocity is parallel to the x axis B) Its acceleration parallel to the x axis C) Both its velocity and its acceleration are parallel to the x axis D) Neither its velocity or its acceleration need be parallel to the x axis

B) Net force causes acceleration, but it does not necessarily say anything about the direction of the velocity. C) The force creates an acceleration in the positive x direction parallel to the x axis. Since the box is accelerating in the positive x direction, the velocity is also in the positive x direction and parallel to the x axis. CheckPoint The net force on a box is in the positive x direction. Which of the following statements best describes the motion of the box : A) Its velocity is parallel to the x axis B) Its acceleration parallel to the x axis C) Both its velocity and its acceleration are parallel to the x axis D) Neither its velocity or its acceleration need be parallel to the x axis

Pre-lecture Question 1:  A lot of requests to go over the first question

Velocity and Acceleration  Acceleration a=dv/dt  Change in velocity:  v= v 1 -v 0 =a x dt  This is a vector equation where  v, v 1, v 0 and a are vectors

Force to stop a car You are a car designer. You must develop a new braking system that provides a constant deceleration. What constant net force is required to bring a car of mass m to rest from a speed of V within a distance of D? X 0 = 0 X F = D V 0 = V V = 0

Getting to Newton’s Third Law How does one apply a force? Applying a force requires another object! –A hammer exerts a force on a nail

Newton’s Third Law “Whenever one object exerts a force on a second object, the second exerts an equal and opposite force” OR “To every action there is an equal and opposite reaction”

Skater Skater pushes on a wall The wall pushes back –Equal and opposite force The push from the wall is a force –Force provides an acceleration –She flies off with some non-zero speed

Walking She pushes on the ground and the ground PUSHES her forward Equal and opposite force

Normal Force Consider a pen sitting on a table: –Is the force of gravity acting on it? –Is the pen accelerating? –What is the Force? What is the difference between a force and the Net Force –What keeps the pen from accelerating? Clearly, there is a second force that keeps it from accelerating Call this the “normal” force!

My laptop has mass m and is sitting on the table. What is the net force acting on the table? A.Net force acting on the table is equal to mg and acts down, g=9.8 m/s 2 B.Net force acting on the table is zero because normal force exerted by the table onto the laptop exactly compensates the force exerted by the laptop (=mg) C.Net force acting on the table is zero because normal force exerted by the floor on the table compensates the force exerted by the laptop on the table. D.Net force acting on the table is F=2mg and acts down because it is a sum of gravity and normal force exerted by the laptop on the table, and each is equal to mg.

Clicker Question A force F is applied to a small block, that pushes a larger block. The two blocks accelerate to the right. Compare the NET FORCE on the block with mass M, to the net force on the block with mass 5M. A) F M < F 5M B) F M = F 5M C) F M > F 5M M F a 5M5M

Clicker Question A force F is applied to a small block, that pushes a larger block. The two blocks accelerate to the right. Compare the NET FORCE on the block with mass M, to the net force on the block with mass 5M. A) F M < F 5M B) F M = F 5M C) F M > F 5M M F a Net Force Same acceleration, so larger mass has larger net force. 5M5M

Pre-Lecture Question 2 ABCDEABCDE

You tie a brick to the end of a rope and whirl the brick around you in a horizontal circle. Which best describes the path of the brick after you suddenly let go of the rope. A.The brick drops directly straight down to the ground. B.The brick continues in its circular path. C.The brick spirals outward. D.The brick flies off in a straight line.

Pre-Lecture Question 2

CheckPoint You are driving a car with constant speed around a horizontal circular track. The net force acting on your car A) Points radially inward toward the center of the circular track B) Points radially outward, away from the center of the circular track C) Points forward in the same direction your car is moving D) Points backward, opposite to the direction your car is moving E) Is zero.

A) Force is in the same direction as acceleration (in this case, centripetal). B) the acceleration is outwards, therefore the force is outwards E) Because the car is moving at a constant speed, so there is no a. We get the net force is zero. C) The car is moving forward so the net force must be forward. CheckPoint Responses You are driving a car with constant speed around a horizontal circular track. The net force acting on your car A) Points radically inward toward the center of the circular track B) Points radically outward, away from the center of the circular track C) Points forward in the same direction your car is moving D) Points backward, opposite to the direction your car is moving E) Is zero.

* They can have also have tangential acceleration if their speed is not constant Aside: Centripetal acceleration and force 1) Objects moving in a circle always have a component of acceleration, called centripetal, which is toward the center of the circle.* 2) Centripetal acceleration must be caused by a force: –Friction, gravity – whatever force keeps it moving in a circle. –This force is often called the “centripetal force” 3) There is no “new” kind of force here. 4) There is no such thing as centrifugal force.

Free Body Diagrams Same tricks as in Chapters 1-3: 1.Draw a diagram: Draw each force on an object separately! Force diagram! 2.Break each force into the X and Y- components, THEN sum!!! –Show your TA that you know the difference between a force, and a component of force –GREAT way to pick up partial credit

Pulling a box FPFP  A box with mass m is pulled along a frictionless horizontal surface with a force F P at angle  as given in the figure. Assume it does not leave the surface. a)What is the acceleration of the box? b)What is the normal force?

2 boxes connected with a string Two boxes with masses m 1 and m 2 are placed on a frictionless horizontal surface and pulled with a Force F P. Assume the string between doesn’t stretch and is massless. a)What is the acceleration of the boxes? b)What is the tension of the strings between the boxes? M2M2 M1M1

A crate is suspended from the end of a vertical rope. The tension in the rope is greater when: A.The crate is at rest. B.The crate is moving up at a constant speed. C.The crate is moving down at a constant speed. D.The tension for A, B and C are the same.