Key Homework Work

NAME……………………..BLOCK……

Module 1: Key Homework: Mechanical Energy [Maximum mark = 30 Grade boundaries: A:25; B:22; C:19; D:15; E:12] 1.The cyclist and cycle shown below have a total mass of 75 kg.

(a) He is cycling at a constant velocity of 15 m s-1 along a flat road straight road. Calculate the total kinetic energy of the cyclist and his bicycle [ 2 marks] (1/2)mv2 = Ek (1/2) x 75 x 152 = 8437.5 (b)(i)State the definition of work [1 mark] (ii)the cyclist and his bicycle are experiencing a total drag force of 80 N. Because he is travelling at a constant velocity, he must be generating a driving force of 80 N. Calculate the useful work done that the cyclist does in one second [1 mark] FS = W 80 x 15 = 80 1200J /s (c)The cyclist now increases his speed to 18 m s-1 from 15 m s-1 (i)Calculate his increase in kinetic energy [1 mark] (1/2)mv2 = Ek (1/2) x 75 x 152 = 8437.5 -

(1/2) x 75 x 182 = 12150 Increase = 3712.5

(ii)To increase his kinetic energy the cyclist had to do some extra work. The useful extra work he did in increasing his speed is equal to the increase in kinetic energy of him and his bicycle. How much of his store of chemical energy (within his body) did he use to increase his speed if the average efficiency of the cyclist and his bicycle is 80%. [2 marks] FS = W -1-

2.The high jumper shown below has a mass of 65 kg and has just cleared a height of 1.9 m.

When standing upright before making the jump her centre of gravity is 1.1 m above the ground. (a)(i)As she clears the bar, by how much has she raised her centre of mass? [1 mark] 1.9 – 1.1 = 0.8 (ii)By how much has her gravitational potential energy increased? [2 marks] MGH 65 x 9.81 x 1.9 = 1211.535 65 x 9.81 x 1.1 = 701.415 Increase = 510.12 (b)(i)State the law of conservation of energy: [2 marks]

Energy may neither be created nor destroyed. The sum of all the energies in the system is a constant. (ii)In reaching her maximum height during the jump, she loses 40 J of energy in overcoming air resistance. Calculate: the amount of kinetic energy that she must have had at take off [1 mark] 1211.535 + 40 = 1251.535 (iii)What is her take off speed? [2 marks] -2-

3. During a bungee jump there is a point at which the bungee starts to be stretched. The stretching force (tension) in the bungee increases until the bungee reaches its maximum extension. Suppose during a bungee jump the tension increases steadily from zero to 800 N during which the bungee increases in length by 12 m. (a)On the axes below sketch a force versus distance graph and include scales on both axes: [2 marks]

(b)Use the graph to determine the work done by the stretching force in stretching the bungee by 12 m [2 marks] 4.On a ski drag lift, the lift cable exerts a force of 400 N on a skier in dragging him up a slope. The cable is at an angle of 40o to the slope and the skier is dragged a distance of 200m along the slope. Calculate (a)the component of the force exerted by the cable in the direction of the slope [2 marks] (b)Calculate the total work done by the component of the force (exerted by the cable) in the direction of the slope in pulling the skier the 200 m distance along the slope [2 marks] -3-

5.The diagram below shows a man of mass 80 kg running up the stairs.

To run up the stairs at a steady speed the man must apply an upward force equal to his weight. He takes 1.2 s to run up the stairs and the height rise is 1.6 m. (a)How much work does he do in achieving a height rise of 1.6 m [2 marks] (b)What is his useful power output in achieving a height rise of 1.6 m [2 marks] 6. The motor boat shown below is travelling at a constant velocity of 3.0 m s-1

The total drag force on the boat as it moves through the water is 200 N. (a)what is the size of the driving force from the propeller? [1 mark] (b)What is the useful output power of the motor driving the propeller ? [2 marks]

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