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XE 121 Engineering Concepts Lecture 2 Force, matter, mechanical systems Dr Nicolas D. D. Miché [email protected] University of Brighton – School of Computing Engineering and Mathematics XE121 - nddm 1 Force, matter, mechanical systems Fundamentals XE121 - nddm 2 Force is a Vector. The SI unit for force is the Newton (N). One Newton of force is equal to 1 kg * m/s2. Force is a quantitative description of the interaction between two physical bodies, such as an object and its environment. Force is proportional to acceleration. In calculus terms, force is the derivative of momentum with respect to time. XE121 - nddm 3 Mass. A measure of the amount of matter contained in or constituting a physical body. In classical mechanics, the mass of an object is related to the force required to accelerate it and hence is related to its inertia, and is essential to Newton's laws of motion. Objects that have mass interact with each other through the force of gravity. XE121 - nddm 4 Acceleration, Acceleration is the rate of change of velocity as a function of time. It is a Vector. In calculus terms, acceleration is the second derivative of position with respect to time or, alternately, the first derivative of the velocity with respect to time. The SI units for acceleration are m / s2 (meters per second squared or meters per second per second). m XE121 - nddm 5 Moments/Torque F ,O M F ,O F r + F r A O M F ,O XE121 - nddm 6 Expressed as Magnitude: r F sin F d More torque with a spanner? More torque with a screwdriver? XE121 - nddm 7 Example: net torque on a cylinder T1 = 5 N R1 = 1 m T2 = 15 N R2 = 0.5 m Calculate the net torque on this system of forces according to the coordinate system shown Quiz XE121-L2-1 XE121 - nddm 8 Measurement of torque: Dynamometer Distance Distance Force (perpendicular) Load cell (force measurement) XE121 - nddm 9 Water (or Froude) dynamometer XE121 - nddm 10 Load Cell XE121 - nddm 11 Friction Static Dry Friction Friction forces occur in the opposite direction to forces tending to move two objects in contact XE121 - nddm 12 If you press a textbook flat against a vertical wall; what is the direction of the friction force exerted by the wall on the book? Quiz XE121-L2-4 • A - downward • B - upward • C - out from the wall • D - into the wall XE121 - nddm 13 The static frictional force cannot exceed a certain magnitude, called the limiting static friction. Fmax ≥ P → Equilibrium Fmax < P → Slippage XE121 - nddm 14 The maximum frictional force between two surfaces is proportional to the normal contact force Fmax N With μ = μs static coefficient of friction when non-slip μ = μk static coefficient of friction for slippage The angle α of the resultant R is specified by tan α = F/N At Fmax, α reaches a max value of φs such as tan s s The limit conditions of friction can be represented within a cone of friction XE121 - nddm 15 A B 30º Quiz XE121-L2-2 30º Which is the easier way to move the sled? • A - pushing from behind, slightly downwards • B - pulling with a rope, slightly upwards • C - either Quiz XE121-L2-3 Why is that? •Answer in a few words XE121 - nddm 16 Slippage / non-slippage Non-slip condition Plane intersecting tan s Direction of potential sliding F ( Fmax s N ) Maximum static friction Plane intersecting tan s F ( Fmax s N ) Slippage Plane intersecting Direction of potential sliding Direction of tan s F Fmax k N XE121 - nddm 17 Some typical coefficients of friction μs μk Steel on Steel (dry) 0.6 0.4 Steel on Steel (grease) 0.1 0.05 Brake pad on Cast iron 0.4 0.3 Teflon on Steel 0.04 0.04 Dry 0.8 0.5 Wet 0.4 Icy 0.1 Tyre on Road Synovial joints in humans XE121 - nddm 0.01 0.003 18 Simple experimental determination of friction coefficients A block of material A remains static on a ramp of material B The y component of the weight of the block (mg cosθ) results in an opposite normal contact force n The x component of the weight of the block (mg sinθ) is opposed by the friction force f The incline angle is increased until the block is on the edge of slipping. At this point the friction force has reached its maximum. XE121 - nddm Therefore, friction coefficient A/B f tan n 19 XE 121 – Engineering Concepts – Mechanical Part Next week •Mechanical links, static equilibrium Dr Nicolas D. D. Miché [email protected] University of Brighton – School of Computing Engineering and Mathematics XE121 - nddm 20