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FYS-MEK1110 - Mechanics

Facts about this course: Credits: 10 Teaching semester: Every spring semester Examination semester: Every spring semester Language of instruction: Norwegian Administrated by: Department of Physics

Detailed course information - Current and previous semesters: Spring 2012 Spring 2011 Spring 2010 Spring 2009 Spring 2008 Spring 2007 Spring 2006 Spring 2005 Spring 2004

Course content

This course provides an introduction to Newtonian mechanics and special relativity, which provides the foundation for further studies in physics. You learn to address motion in one, two, and three dimensions: Newton’s laws of motion; Force models for gravitation, viscous force, and spring force; Curved motion and rotation; Linear momentum; Angular momentum and torque; Multi-particle systems and rigid bodies; Newton’s second law for rotational motion; Conservation laws for linear and angular momentum and mechanical energy; Fictive forces; Simple linear elasticity theory; Special relativity.

Learning outcomes

After the course, students should be able to:

Motion:

• Describe motion in one, two, and three dimensions graphically, mathematically, and numerically; Interpret graphical and mathematical descriptions of motion; Apply the definitions of velocity and acceleration to find the equations of motion
• Apply the equations of motion to determine the motion of an object using analytical and numerical methods: with given velocity or acceleration using both analytical and numerical methods: with an arbitrary expression for velocity or acceleration using numerical methods; and solve and interpret the equations of motion for damped and periodic motion

Newton’s laws of motion:

• Use free-body diagrams to find the forces acting on an object - Apply Newton’s second law to find the equations of motion for an object or a system of objects
• Know force models for constant force, drag force, spring force, and gravitation; Apply these models as approximations of more general forces; Apply an arbitrary force law to find the equations of motion
• Apply Newton’s laws to find forces for a given motion: interpret the applicability of such an approximation, and apply the approximation to discuss string- or normal forces
• Know force models for dynamic and static friction; Use the models to find the equations of motion for an object; and Solve the equations using analytical and numerical methods

Work and energy:

• Define mechanical work and its relation to mechanical energy; Apply the work-energy-theorem for the force models mentioned above
• Define potential energy and conservative forces; Know the potentials for a constant force, a spring force, and the gravitational force; Use energy-arguments to solve problems with conservative forces, with non-conservative forces that do no work, and with non-conservative forces that do work
• Interpret an energy diagram; Apply an energy diagram to find equilibrium points; Sketch and interpret motion in an energy diagram; Relate potential energy to forces
• Define power; Apply the definition to find the power during a motion; Solve problems with given power consumption

Linear momentum:

• Define linear momentum for an object and a system of objects; Relate linear momentum to impulse and average force during a collision; Apply the conservation of linear momentum to relate initial and final conditions during a collision; Know the definition of the coefficient of restitution, elastic, inelastic, and perfectly inelastic collisions; and know how to apply these concepts on collision problems
• Know and apply the rocket equation

Multiparticle-systems and rigid bodies:

• Define the center of mass for a multi-particle system; Find the center of mass for simple and compound objects using summation, and analytical and numerical integration
• Apply Newton’s law of motion for multi-particle systems in the same way as Newton’s law of motion for point particles
• Define potential and kinetic energy in a multi-particle system: Apply energy partitioning; Know the potential energy of a multi-particle system in a constant force field; Apply the conservation of energy to solve problems with multi-particle systems

Rotation, angular momentum, and torque:

• Describe rotation of a rigid body in two and three dimensions; Apply the definition of angular velocity and angular acceleration to determine the equations of motion for a rotating body in two dimensions; Solve the equations of motion for the angle of rotation analytically and numerically (just as for position)
• Define angular momentum and torque; Apply Newton’s law for rotational motion for a point particle
• Define the moment of inertia, torque, and their relation for a point particle
• Define the moment of inertia for a multi-particle system and for a rigid body; Determine the moment of inertia by summation, by the parallel-axis theorem, and by analytical and numerical integration
• Apply Newton’s second law for rotational motion around the center of mass and around a fixed point for a multi-particle system and a rigid body to find the equations of motion
• Apply the conservation laws for angular momentum to problems with collisions
• Define potential and kinetic energy for multi-particle systems and rigid bodies; Apply energy considerations to motion and collisions
• Relate translational and rotational motion for coupled systems such as in rolling motion

Other subjects:

• Know the fictive forces acting in a rotating coordinate system; Apply fictive forces to interpret forces and motion in an accelerated system such as at the surface of the Earth
• Define stress, strain, Young’s modulus and Poisson’s ratio; Relate these concepts to forces and deformations of objects
• Define an event (in time and space); Apply the Lorentz-transformations for position and velocity; Apply the transformations to explain length contraction and time dilation effects; Define relativistic mass, momentum, and energy

General:

• Apply and evaluate the use of several solution strategies for a specific physical problem; Introduce and evaluate approximations to the problem; discuss the validity of a solution found using a particular strategy
• Evaluate, discuss, and interpret results from analytical and numerical solutions of a physical problem; Relate the results to the real world
• Write programs that solve the equations of motion; visualize the solutions; compare with simplified, analytical solutions, and review your results

Admission

Students at UiO must apply for courses in StudentWeb.

International applicants, if you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures for international applicants.

Prerequisites

Formal prerequisites

In addition to fulfilling the Higher Education Entrance Qualification, applicants have to meet the following special admission requirements:

One of these:

• Mathematics R1
• Mathematics (S1+S2)

And and in addition one of these:

• Mathematics (R1+R2)
• Physics (1+2)
• Chemistry (1+2)
• Biology (1+2)
• Information technology (1+2)
• Geosciences (1+2)
• Technology and theories of research (1+2)

The special admission requirements may also be covered by equivalent studies from Norwegian upper secondary school or by other equivalent studies. Read more about special admission requirements.

Recommended prior knowledge

MAT-INF1100 - Modelling and computations, MAT1100 - Calculus and INF1100 - Introduction to programming with scientific applications. Knowledge of high school physics is strongly recommended.

Overlap

10 credits overlap against FYS-MEF1110 - Mekanikk for MEF and FY-ME100.

Teaching

The course extends over a full semester with 7-8 hours of teaching per week (lectures and problem solving). A total of 5+1+5 compulsory exercises are to be handed in, and out of these a total of 3+1+3 must be passed. Students that have given answers on more than 3/4 of the "klikker"-questions can skip one compulsary delivery.

Exam information

Written final exam (4 hours). A total of 5+1+5 compulsory exercises are to be handed in. Students that have given answers on more than 3/4 of the "klikker"-questions can skip one of the compulsory exercises.

For detailed information about examinations at the Faculty of Mathematics and Natural Sciences please see http://www.matnat.uio.no/english/studies/index.html

This subject offer new examination in the beginning of the subsequent term for candidates who withdraw during an ordinary examination or fail an ordinary examination. For general information about new examination, see http://www.mn.uio.no/studier/admin/eksamen/utsatt-og-ny-eksamen/index.html
and www.matnat.uio.no/english/studies/examination/repeat.html

Exam resources

Øgrim and Lian or Angell and Lian: "Fysiske størrelser og enheter". Rottman: "Matematisk formelsamling". Approved calculator.

Assessment and grading

Course grades are awarded on a descending scale using alphabetic grades from A to E for passes and F for fail. Read more about the grading system .

Evaluation of this course

Feedback from our students is essential to us in our efforts to ensure and further improve the high quality of our programmes and courses. As a student at the University of Oslo you will therefore be asked to participate in various types of evaluation of our courses, facilities and services. All courses are subject to continuous evaluation. At regular intervals we also ask students on a particular course to participate in a more comprehensive, in-depth evaluation of this course, a so called "periodic evaluation".

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