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 1)Choose system (object or group) 2)Draw forces acting on object -action at a distance - Gravity -contact - things touching 05

Free Body Diagrams 06

Free Body Diagrams 06

Free Body Diagrams 07

Free Body Diagrams 07 Always, always, always start with a free body diagram. Do not write any equations before you have drawn all the forces in a free body diagram!

Tension Force Direction: Parallel to rope, always pulling. Magnitude: As much or little as needed for F net =ma 08 m2m2 m1m1 g Demo: 2 skateboards + rope

Checkpoint 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 I drew a FBD and then I wrote down the equation for newton's law. Using this I determined that T=mg+ma 09 BOX IN THE ELEVATOR!!! OMG

Tension ACT 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? A) 0 lbs. B) 4 lbs. C) 8 lbs. mmm ? 12

Normal Force "It is what it has to be to do what it does" !!?? Normal force is the force perpendicular to the surface that prevents the objects from passing through each other. 1) 1)Direction: Perpendicular to surface and out 2) 2)Magnitude: As much or little required keep objects separate. 13

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. There are only two forces acting on the box. Gravity is the arrow pointing down and the normal force is the upward arrow. 14

ACT 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. AB C D 16

Spring Force Direction: Parallel to spring: Push or pull Magnitude:F=-kx 16 Demo: Hooke’s Law blackboard

Springs Example I would like to have more examples with the spring force. PLEASE! 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 mB) 2 m C) 5 m 20

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 m a L 22

ACT 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 24 V

ACT 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 26

ACT A cart with mass m 2 is connected to a mass m 1 using a string that passes over a frictionless pulley, as shown below. The cart is held motionless (a = 0). The tension in the string is A) m 1 g B) m 2 g C) 0 m2m2 m1m1 g a = 0 29

ACT A cart with mass m 2 is connected to a mass m 1 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. After the cart is released, the tension in the string is A) = m 1 g B) > m 1 g C) < m 1 g m2m2 m1m1 g a 35

Universal Gravitation Could we talk a little bit more about the Newton gravitational force formula and its relation with g? Near surface of earth r=R earth Direction: Toward other object (down near earth surface) Magnitude:F=GMm/r 2 (mg near earth surface) 40

General Comments 40 The spring example, if the elevator is accelerating upwards, then the box is accelerating downwards? so the force of what causes the box to go downwards? Explain tension in a spring, and whether the length of the spring increases or decreases based upon tension. It makes sense when real world scenarios are considered, but what is the scientific explanation of it? Tension please especially the whole elevator thing. Nothing too intense.