Midterm Exam #1

1. Midterm Exam #1 • First midterm is next Friday, January 31 (75 minutes!!!) • Units 1-5: 1D kinematics – Forces and FBDs (todays lecture) • Things to bring:Pencil, calculator, 1 sheet of notes (8.5 X 11 in., front & back) • Bring your U of U ID card: you will not receive a grade unless you show it upon turning in your exam • No makeups!!! (Unless you are unavailable due to University/military business or documented medical emergency) • Cheating: You will receive a zero and referred to the University administration – may result in an “E” for the course and expulsion • You must contact Prof. Gerton by Monday, January 27 if you have a conflict wit the exam times/days!!!

2. Announcements • Second quiz on Friday in class (no more than 12 minutes) • Newton’s Laws: Solutions to group problems are on the Schedule page of the website • You will need NOTHING except a writing instrument and calculator • You must provide your TA’s name if you want to get your quiz back • You MUST write down your seat number: we will not give you a grade if you don’t provide this. • No makeups!!! (That’s why I have the 83 point buffer)

3. Classical Mechanics Lecture 5: Forces & Free-Body Diagrams Today's Concepts: a) Free Body Diagrams b) Force due to strings c) Force due to springs d) Force due to gravity

4. How to determine the box’s acceleration…

5. How to determine the box’s acceleration… • Identify the forces acting only on the box • Draw a free-body diagram (FBD) for the BOX (a visual CATALOG of forces)

6. How to determine the box’s acceleration… • Identify the forces acting only on the box • Draw a free-body diagram (FBD) for the BOX (a visual CATALOG of forces) • Apply Newton’s 2nd Law

7. Free Body Diagrams: Your Concerns • The concept of which forces are present to put on a free body diagram. • More difficult problems with multiple directions of forces. • I can sometimes get confused in finding the direction of my force diagram vectors. I often put the arrows facing the opposite direction they should be. • Boxes and free body diagrams.

8. F1 F1 The net force on an object is the sum of all forces on the object responsible for the object’s acceleration FBDs, Net Force, and Acceleration Individual Forces Add ‘em up (tip-to-tail) What’s the acceleration?

9. Gravity: Your Concerns • If the gravitational constant is at all important there should have been more emphasis upon it. It was an extremely complex explanation distilled into two minutes, leaving me thoroughly confused. • i found the example of the gravitational pull between the planets to be hard to understand…

10. Force due to Gravity Near Earth’s surface: m An object’s weight force is always directed toward the Earth’s center Earth Center of Earth

11. Force due to Gravity Near Earth’s surface: m An object’s weight force is always directed toward the Earth’s center Earth Center of Earth

12. Support Forces: Normal Force and Tension • A support force is simply what it has to be to do what it does! • It can simply support an object (keep it from passing through another) • It can accelerate an object • Magnitude is determined by Newton’s 2nd Law!

13. Springs • A spring exerts a “Restoring Force” if it is deformed • If stretched: force acts to shorten spring • If compressed: force acts to elongate spring • Magnitude of the force is proportional to amount of deformation: if x0 = 0

14. Revote: Box in an Elevator (Spring) a L m Analysis: Newton II: Must be > 0 A box of mass mis hung by a spring from the ceiling of an elevator. When the elevator is at rest the length of the spring is L0= 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

15. ACT: Going Up, Slowing Down 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 Analysis: -

16. ACT: Elevator Scale Analysis: Need downward acceleration Scale reads low 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) Your usual weight B) More than your usual weight C) Less than your usual weight

17. 250 of 250 26 Revote: Box Free Body Diagram The only forces acting on the box are gravity (acting downward) and the normal force (acting upward). 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.

18. 250 of 250 26 ACT: Inclined Plane D A B C • No friction: no force parallel to plane • Gravity always acts downward! • Net force is down the ramp A block slides 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.

19. ACT: A Hanging Mass The tension in the string is A) m1g B) m2g C) 0 m2 Analysis: m1 m1 A cart with mass m2is connected to a mass m1using a string that passes over a frictionless pulley, as shown below. The cart is held motionless.

20. ACT: A Hanging Mass part II After the cart is released, the tension in the string is A) = m1g B) > m1g C) < m1g a m2 m1 A cart with mass m2is connected to a mass m1using 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.

21. ? Last ACT m m m A) 0 lbs.B) 4 lbs.C) 8 lbs. 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?