14 14 Grasshoppers can jump up to twenty times their length to escape predators. The magnitude of the launch velocity v does not vary significantly for a given grasshopper, so the length of the jump mostly depends on the launch angle θ. The diagram shows a grasshopper at the instant it launches. v θ (Source: adapted from http://gclipart.com/grasshopper-clipart_28241/) (a) The grasshopper jumps from rest on level ground. The launch velocity is 2.6 m s−1 at an angle of 57° to the horizontal. (i) Show that the vertical component of the launch velocity is about 2 m s−1. 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(ii) Assess whether the horizontal distance travelled by the grasshopper in the jump is about 20 times the grasshopper’s length. length of grasshopper = 5.0 cm (5) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. Turn over 15 (b) Grasshoppers with longer legs accelerate to their launch velocity over a longer time. Leg length has a negligible effect on both the mass of a grasshopper and the energy released in a jump. Explain how leg length affects the force exerted on the ground during a jump. 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(c) In a recent study it was discovered that grasshoppers, living in an environment with hunting spiders, increase their launch velocity on average by 20%. The jump length of these grasshoppers was more than doubled. Assess whether a 20% increase in launch velocity alone is sufficient to double the jump length. 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(Total for Question 14 = 14 marks) TOTAL FOR SECTION A = 54 MARKS 16 BLANK PAGE Turn over 17 SECTION B Answer ALL questions in the spaces provided. 15 A force meter measures force by making use of Hooke's Law. The extension of a spring inside the force meter allows the magnitude of the force applied to be read from a scale. (a) The spring in one type of force meter extends by 5.5 cm when a force of 2.5 N is applied. (i) Show that the stiffness of the spring is about 50 N m−1. 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(ii) Two identical force meters of this type support a mass of 0.400 kg as shown. Diagram not to scale 60° 0.400 kg (Source: adapted from https://image.slidesharecdn.com/ balancedunbalancedgravityfriction-170509114658/95/balanced-unbalanced-gravity- friction-14-638.jpg?cb=1494330595) Calculate the extension ∆ x of each spring. (4) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ∆ x = ...................................................... 18 *(b) A beaker of water is placed on a balance and a rock is hung from a force meter as shown in diagram 1. The initial reading on the balance is R, and the initial reading on the force meter is F. The rock is lowered gently into the beaker of water until it is completely submerged. Diagram not to scale rock water balance Diagram 1 Diagram 2 (Source: adapted from https://passnownow.com/wp-content/uploads/2014/06/upthrust) Turn over 19 Explain any changes in the readings R and F as the rock is lowered into the water as shown in diagram 2. 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(Total for Question 15 = 12 marks)