* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download further force and motion considerations
Survey
Document related concepts
Coriolis force wikipedia , lookup
Equations of motion wikipedia , lookup
Center of mass wikipedia , lookup
Relativistic mechanics wikipedia , lookup
Modified Newtonian dynamics wikipedia , lookup
Classical mechanics wikipedia , lookup
Jerk (physics) wikipedia , lookup
Hooke's law wikipedia , lookup
Newton's theorem of revolving orbits wikipedia , lookup
Nuclear force wikipedia , lookup
Fictitious force wikipedia , lookup
Fundamental interaction wikipedia , lookup
Seismometer wikipedia , lookup
Rigid body dynamics wikipedia , lookup
Centrifugal force wikipedia , lookup
Classical central-force problem wikipedia , lookup
Transcript
Advanced Programming for 3D Applications CE00383-3 Forces in Human Motion Lecture 4 Bob Hobbs Staffordshire university Modelling forces Types of force • Applied Load • Tension Tension • Contact: • Friction: • Bouyancy: • Drag: 3 F FT Fc = kx Ff = mN Fb = rVg Fd = ACdv Applied loads • Normally act on one point • Typically – Objects hanging from ropes – Objects being pushed – Objects being pulled F 4 Example 1 A mass of 25 kg is hung from a bar by a hanger. Determine the applied load? +y F = (m*g) = (25 * -9.81) = -245.25 N 25 kg 5 Tension • The internal force acting within a – rope – cable – wire – component in a framework T 6 Always PULLING Always +ve Example 2 A mass of 25 kg is hung from a bar by a hanger. Determine the tension in the hanger? FT +y 25 kg 7 FT = (m*g) = (25 * -9.81) = 245.25 N 25 kg Contact • Whenever two bodies touch each other there is a contact force – Always normal to the surface – A REACTION force – Sometimes modelled using stiffness R 8 Example 3 A block of mass 75 kg is placed on a floor. What is the reaction force? Applied force, F = mg = (75 * -9.81) = -735.75 N Reaction force = -F = 735.75 N +y 9 Block “pushing” on the floor Floor pushing on the block Friction • Another force associated with contact – Parallel with the surface – Opposes motion – Ff = mN 10 Example 4 What is the maximum friction force exertable when a car, of mass 2000 kg, has been fitted with tyres of m =0.3? Reaction, N = -F = 20.36 kN +y Using Ff = mN = 0.3 * 20.36x103 = 6.1 kN 11 F = mg = 2000 * -9.81 = -20.36 kN m? • Coefficient of friction Ff Block starts to slide when gravity overcomes friction q m = tan(q) 12 Example 5 A block is placed on a sliding table. The block begins to slide when the table reaches an angle of 25o. Determine the coefficient of friction. Using m = tan(q) = tan(25) = 0.466 13 Stiffness • All objects act as springs • The restoring force is proportional to deflection x Force pulling the spring Spring pulling on the object Fs = k*x 14 Stiffness coefficient + Applied force, F (N) + + + + + + Fax F = k*x k = DF/Dx (N/m) + + + 15 deflection, x (m) Example 6 A spring is subjected to an applied load of 750 N. The spring extends by 25 mm. Determine the stiffness of the spring. Unloaded spring 25 mm 750 N Using k = DF/Dx = 750 / 0.025 = 30 kN/m 16 Stiffness • A spring under Tension PULLS • A spring under Compression PUSHES 17 String, Cables and Ropes • They can only PULL • You may assume constant tension throughout. 18 Dampers (Viscous) Opposing force generated proportional to v I.e. F = cv where c is the damping coefficient Body moves with velocity v 19 Impact forces F = constant; F =Dp/t Dp = change in momentum General Area = Dp Triangular form F = 2Dp/t Sine wave F = p/2 Dp/t 20 Compression- Tension Cycle 21 Ground Reaction Force • Newton's Law of Gravitation: – any two objects with masses attract each other and the magnitude of this attracting force is proportional to the product of the masses and inversely proportional to the square of the distance. This also holds for the gravitation between the earth and an object on the earth. The gravitational force acted upon an object by the earth is called gravity or weight of the object. • Newton's Law of Reaction: – there is an equal and opposite reaction to every action. In other words, the action to the ground is always accompanied by a reaction from it. This reaction force from the ground is called the ground reaction force (R). The ground reaction force is an important external force acting upon the human body in motion. We use this force as propulsion to initiate and to control the movement. • Newton's Law of Acceleration: – the external forces acting on the body causes an acceleration: 22 Ground Reaction Force F = m·a [1] where F = sum of external forces (vector), m = mass of the subject (scalar), and a = acceleration (vector) of the subject's centre of mass (CM). F=R+W [2a] Here, note that weight W always acts downward. Considering only the vertical forces and their directions: Fz = Rz - W [2b] where Fz = net vertical force acting on the body, Rz = the vertical ground reaction force, and W = weight of the body. From [1] and [2b]: Rz - W = maz [2c] where az = magnitude of the vertical acceleration. Rearranging [2c], we obtain 23 az = ( Rz - W ) / m [3] Impulse and Momentum • During step sequence • • 24 – Average net Force = mass * average acceleration – Acceleration = change of velocity Force over a period of time causes a change of momentum over that time. – Average net force over a period of time = m(Vf – Vi) Therefore changing momentum over a short period of time generates a greater force than over a longer period of time – When landing from a height the start and finish velocities are the same - as is the mass – whether you land stiff-legged or ‘bounce’ Impact • The first peak is called the impact peak (P1) while the second is called the propulsion peak (P2). The impact peak is associated with the impact of the foot to the ground during early foot contact phase. The propulsion peak is associated with the propulsion of the body forward. It has always been the main focus of the shoe engineers that how to design the shoe-sole to reduce the impact peak while maintaining the propulsive characteristics. 25 Reduce impact by 1. Cushioning 2. Alter gait 26