Classical Mechanics Midterm 2 Review Force and Energy Midterm this Friday March 13 Classical Mechanics Midterm 2 Review Force and Energy Newton’s Laws of Motion Forces and Free Body Diagrams Friction Work and Kinetic Energy Conservative Forces and Potential Energy Work and Potential Energy Knowledge of Units 1-3 will be useful “Playing with Blocks”

Midterm Exam Multiple choice…but show your work and justification. Calculations Forces and Free-Body Diagrams Weight and Pulleys Springs Friction Gravitational Normal Work Calculations Conservation of Energy Conceptual questions…like checkpoint problems. Bring calculators and up to five sheets of notes

Midterm Exam 2 Sample exam Folder under Files menu on PHYS1500 Canvas Website Phys 1500 Exams https://utah.instructure.com/courses/320947/files - Spring 2013: http://www.physics.utah.edu/~springer/phys1500/exams/MidtermExam2.pdf - Solutions: http://www.physics.utah.edu/~springer/phys1500/exams/MidtermExam2Soln.pdf - Long Sample: https://utah.instructure.com/courses/320947/files/45779670/download?wrap=1 - Long Solutions:https://utah.instructure.com/courses/320947/files/45802143/download?wrap=1 Phys 2210 Exams - Practice : http://www.physics.utah.edu/~woolf/2210_Jui/rev2.pdf - Spring 2015: http://www.physics.utah.edu/~woolf/2210_Jui/ex2.pdf

Force and Energy Summary

(otherwise objects velocity is constant) Determining Motion Force Energy Unbalanced Forces  acceleration (otherwise objects velocity is constant) Total Energy  Motion, Location Determine Net Force acting on object Work Motion from Energy conservation Use kinematic equations to determine resulting motion

Unit 4: Newton’s Laws

Unit 5: Forces and Free-Body Diagrams Box

Inventory of Forces Weight Normal Force Tension Gravitational Springs …Friction

Force Summary

Unit 6: Friction

Friction

Unit 7: Work and Kinetic Energy

Work-Kinetic Energy Theorem The work done by force F as it acts on an object that moves between positions r1 and r2 is equal to the change in the object’s kinetic energy: But again…!!!

The Dot Product

Vectors!!!

Unit 8: Conservative Forces & Potential Energy

Unit 8: Conservative Forces & Potential Energy

Unit 9:Work and Potential Energy

Energy Conservation Problems in general For systems with only conservative forces acting Emechanical is a constant

Gravitational Potential Problems conservation of mechanical energy can be used to “easily” solve problems. Define coordinates: where is U=0? Add potential energy from each source. as

Example Problem : Block and spring A 2.5 kg box is held released from rest 1.5 m above the ground and slides down a frictionless ramp. It slides across a floor that is frictionless, except for a small section 0.5 m wide that has a coefficient of kinetic friction of 0.2. At the left end, is a spring with spring constant 250 N/m. The box compresses the spring, and is accelerated back to the right.   What is the speed of the box at the bottom of the ramp? What is the maximum distance the spring is compressed by the box? Draw a free-body diagram for the box while at the top of the incline ? When the spring is maximally compressed? When the box is sliding on the rough spot to the right? What is the total work done by friction? Each way? What height does the box reach up the ramp after hitting the spring once? Where will the box come to rest? 2.5 kg h=1.5 m d = 0.50 m mk = 0.4 k=250 N/m

Example Problem: Free-Body Diagram 1) FBD N T m2 g f T m1 m1 m2g m1g

Example Problem: Free-Body Diagram 1) FBD 2) SF=ma N T m2 g f T m1 m1 m2g N = m2g m1g T – m m2g = m2a m1g – T = m1a add m1g – m m2g = m1a + m2a m1g – m m2g a = m1 + m2

Example Problem: Free-Body Diagram 1) FBD 2) SF=ma N T m2 g f T m1 m1 m2g m1g m1g – T = m1a m1g – m m2g T = m1g – m1a a = m1 + m2 T is smaller when a is bigger

Example Problems

Example Problem

Block

Pushing Blocks

Example Problems

Example: Pendulum h h Conserve Energy from initial to final position.

Example Problems

Example: Pulley and Two Masses A block of mass m1 = 1 kg sits atop an inclined plane of angle θ = 20o with coefficient of kinetic friction 0.2 and is connected to mass m2 = 3 kg through a string that goes over a massless frictionless pulley. The system starts at rest and mass m2 falls through a height H = 2 m.   Use energy methods to find the velocity of mass m2 just before it hits the ground? H = 2 m H m2 = 2  kg m1 θ m2

Example Problems

Example Problems

Force and Energy Summary