Physics 211 Lecture 5 Today’s Concepts: a) Free Body Diagrams b) Force due to strings c) Force due to springs d) Force due to gravity

Classical Mechanics Free Body Diagrams   Free Body Diagrams 1)Choose system (object or group) 2)Draw forces acting on object -Gravity -Things touching (contact) T m mg FREE BODY DIAGRAMS! What can I consider a force?

Free Body Diagrams

Free Body Diagrams

Free Body Diagrams

Tension Force Direction: Parallel to rope, always pulling. Magnitude: As much or little as needed for Fnet=ma T m mg

Checkpoint BOX IN THE ELEVATOR A box of mass m is hung with a string from the ceiling of an elevator that is accelerating upward. Which of the following best describes the tension T in the string: A) T < mg B) T = mg C) T > mg a Fnet = mass*acceleration. Because the elevator is accelerating upward, there is a net force directed upward as well. This means the force pulling the elevator up (tension) is greater than it is down (gravity). Since the elevator is accelerating upward, the tension on the box has to be greater than the gravitational force acting on the box, T - mg = ma

Watch out for subtle mistakes… Many people got the right answer with explanations like this one: m mg T a The elevator is accelerating upward, so not only will gravity pull down on the box, but also the acceleration of the elevator as well.

Tension Clicker Question A block weighing 4 lbs is hung from a rope attached to a scale. The scale is then attached to a wall and reads 4 lbs. What will the scale read when it is instead attached to another block weighing 4 lbs? m ? A) 0 lbs. B) 4 lbs. C) 8 lbs.

Normal Force Normal force is the force perpendicular to the surface that prevents the objects from passing through each other. Direction: Perpendicular to surface and out Magnitude: As much or little required keep objects separate. "The normal force is simply what it has to be to do what it does.“ Oh God, what doe this mean??

Checkpoint A block sits at rest on a horizontal frictionless surface. Which of the following sketches most closely resembles the correct free body diagram for all forces acting on the block? Each arrow represents a force. A B C D If an object is sitting at rest on a frictionless surface, then the only forces acting upon it are the gravitational force and the normal force 250 of 250 26 11

Clicker Question A block accelerates down a frictionless inclined plane. Which of the following sketches most closely resembles the correct free body diagram for all forces acting on the block? Each arrow represents a force. A B C D 250 of 250 26 12

Spring Force Direction: Parallel to spring: Push or pull Magnitude:F=-kx

Springs Example How to actually solve for something like the spring problem would be nice A 5 kg mass is suspended from a spring with spring constant 25 N/m. How far is the spring stretched from its equilibrium position? A) 0.5 m B) 2 m C) 5 m

Checkpoint A box of mass m is hung by a spring from the ceiling of an elevator. When the elevator is at rest the length of the spring is L = 1 m. If the elevator accelerates upward the length of the spring will be: A) L = 1 m B) L < 1 m C) L > 1 m a L m The spring must exert a greater force on the box because T>mg so its length will increase proportionally.

Student Comment/Question I feel really comfortable with these concepts. There is an interesting example that we encountered last year in high school physics with a person standing on a scale in an elevator. The question was when does the personal weigh the most (i.e. when does the scale read the heaviest)? I was wondering about the explanation for that question. V

Clicker Question You are traveling on an elevator up the Sears tower. As you near the top floor and are slowing down, your acceleration A) is upward B) is downward C) is zero V

Clicker Question You are traveling on an elevator up the Sears tower, and you are standing on a bathroom scale. As you near the top floor and are slowing down, the scale reads A) More than your usual weight B) Less than your usual weight C) Your usual weight

Clicker Question A cart with mass m2 is connected to a mass m1 using a string that passes over a frictionless pulley, as shown below. The cart is held motionless. m2 The tension in the string is A) m1g B) m2g C) 0 m1 19

Clicker Question A cart with mass m2 is connected to a mass m1 using a string that passes over a frictionless pulley, as shown below. Initially, the cart is held motionless, but is then released and starts to accelerate. a m2 After the cart is released, the tension in the string is A) = m1g B) > m1g C) < m1g a m1 20

Universal Gravitation Direction: Toward other object (down near earth surface) Magnitude:F=GMm/r2 (mg near earth surface) Newtons relation of the earths gravity to the gravitational forces between two objects was difficult to follow. Near surface of earth r=Rearth

Most of it was really easy to understand Most of it was really easy to understand.... the only problem are the gravity examples.. we should do more of those....

USE ALGEBRA! F = GMm/r^2 careful r = (1+2.2)r G*mmars/(3.2*rmars)^2

Careful, check units. Asks for time in hours, not seconds! Careful, asks for answer in hours! Careful, check units. Asks for time in hours, not seconds!