Turn over 21 17 Some sports place high stresses on the bones in the body, which can result in injury. (a) A gymnast of mass 45 kg dismounts from a beam. Her centre of mass is displaced through 1.6 m vertically before her feet touch the ground. As she lands, the bones in the lower part of her legs experience a force from the ground. The time between hitting the ground and coming to rest is 0.90 s. (i) Calculate the mean force from the ground on the gymnast. 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Mean force from the ground = ....................................................... (ii) Explain how bending both knees when landing helps the gymnast prevent an injury. (3) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. 22 (b) The graph shows how stress varies with strain for normal bone and for unhealthy bone. normal bone unhealthy bone Strain Stress Describe how the graph shows that unhealthy bone under stress is more likely to break than normal bone. 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(Total for Question 17 = 10 marks) TOTAL FOR SECTION B = 24 MARKS TOTAL FOR PAPER = 80 MARKS Turn over 23 List of data, formulae and relationships Acceleration of free fall g = 9.81 m s–2 (close to Earth’s surface) Electron charge e = –1.60 × 10–19C Electron mass me = 9.11 × 10–31kg Electronvolt 1 eV = 1.60 × 10–19J Gravitational field strength g = 9.81 N kg–1 (close to Earth’s surface) Planck constant h = 6.63 × 10–34J s Speed of light in a vacuum c = 3.00 × 108m s–1 Mechanics Electricity Potential difference V W Q = Resistance R V I = Electrical power and energy P = VI P = I 2R P V R = 2 W = VIt Resistivity ρl R A = Current I Q t = ∆ ∆ I = nqvA Kinematic equations of motion s u v t = + ( ) 2 v = u + at s = ut + 1 2 at2 v2 = u2 + 2as Forces ΣF = ma g F m = W = mg moment of force = Fx Momentum p = mv Work, energy and power ΔW = FΔs Ek = 1 2 mv2 ΔEgrav = mgΔh P E t = P W t = efficiency = useful energy output total energy input efficiency = useful power output total power input 24 Materials Waves and Particle Nature of Light Wave speed v = fλ Speed of a transverse wave on a string T v μ = Intensity of radiation I P A = Power of a lens P f = 1 P = P1 + P2 + P3 + … Thin lens equation 1 u + = 1 1 v f Magnification for a lens m v u = = image height object height Diffraction grating nλ = d sin θ Refractive index n1 sin θ1 = n2 sin θ2 n c v = Critical angle sin C n = 1 Photon model E = hf Einstein’s photoelectric equation hf = ϕ + ½mv 2 max de Broglie wavelength λ = h p Density m ρ V = Stokes’ law F = 6πηrv Hooke’s law ΔF = kΔx Young modulus Stress F σ A = Δ Strain x ε x = σ E ε = Elastic strain energy ΔEel = 1 2 FΔx