5 - ELASTICITY

• What is elasticity in materials?

  Property to return to original shape
• What happens if the applied force exceeds the elastic limit?

  The body cannot return to its original shape
• What can a large force cause in materials?

  Rupture of tissues and breakage of bones
• How is stress defined in materials?

  Stress is force per unit area
• What does strain represent in materials?

  Change in an object when stress is applied
• What is the formula for stress?

  $S =$$\frac{F}{A}$
• What is normal strain?

  Change in length to original length ratio
• What are the types of strain according to loading?

  • Normal Strain
  • Compressive: increase in area, decrease in length
  • Tensile: decrease in area, increase in length
  • Shear Strain: change in tangential angle
  • Volumetric Strain: change in volume
• What does Hooke's Law state?

  Ratio of stress to strain is constant
• What happens in the region O to A on the stress-strain graph?

  Material follows Hooke's Law and returns to shape
• What occurs between points A and B on the stress-strain graph?

  Material is elastic but not following Hooke's Law
• What does the region B to D indicate on the stress-strain graph?

  Material is in the plastic region and remains deformed
• What does point E represent on the stress-strain graph?

  Ultimate fail point or breaking point
• What is longitudinal strain?

  Fractional change in length
• What is the formula for longitudinal strain?

  $S_t \equiv \frac{\Delta l}{l}$
• What is Young's Modulus?

  Ratio of stress to strain
• What is the formula for Young's Modulus?

  $Y =$$\frac{S}{S_t}$
• What does the spring constant represent?

  Constant of proportionality for spring force
• What is the formula for the force required to stretch or compress a spring?

  $F =$$-k\Delta l$
• What does the negative sign in the spring force formula indicate?

  Force acts opposite to compression or elongation
• What is the formula for energy stored in a spring?

  $E =$$\frac{1}{2}k(\Delta l)^2$
• How is an elastic body analogous to a spring?

  Force is proportional to stress and strain
• How can energy considerations help estimate injury risk?

  By knowing maximum energy absorption capacity
• What is the formula for the force that will fracture a bone?

  $F_B =$$S_BA =$$YA\Delta l$
• What is the formula for compression at the breaking point?

  $\Delta l =$$\frac{S_B l}{A}$
• What is the formula for energy stored in the bone at the failure point?

  $E =$$\frac{1}{2}Y A l (\Delta l)^2$
• What is the significance of bending joints when jumping?

  Distributes energy to reduce fracture risk
• What are impulsive forces?

  Short duration force in sudden collision
• How is the average value of impulsive force calculated?

  $F_{av} =$$\frac{m v_f - m v_i}{\Delta t}$
• What is momentum?

  Product of mass and velocity
• What is the average force during a collision lasting 0.006 s with a change in momentum of 2 kgm/s?

  $F_{av} =$$3.3 \times 10^2 N$
• How does the magnitude of impulsive force relate to collision time?

  Proportional to change in momentum, inversely to time
• What is the formula for average impact force when falling from height h?

  $F_{av} =$$\frac{W}{\Delta t} \sqrt{\frac{2h}{g}}$
• What is the formula for height h that produces an impulsive force?

  $h =$$\frac{1}{2g} \left(\frac{F \Delta t}{m}\right)^2$
• What is the height of a fall that causes a fracturing average impact force for a 70-kg person?

  $h =$$41.6 cm$
• What is the purpose of airbags in automobiles?

  To stop passengers during sudden impact
• How does an airbag reduce injury risk?

  By decelerating passengers over a distance
• What is the formula for the force that produces deceleration in an airbag?

  $F =$$m a =$$\frac{mv^2}{2s}$
• What is the average stopping force for a 70-kg person at 70 km/hr?

  $F =$$44200 N$
• Why do airbags deflate immediately after deployment?

  To not impede driver control of the vehicle