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SN Kansagra School MECHANICS UNIT TEST Standard: 10 Maximum Marks: 40 Date: 31st August 2016 Time: 60 minutes Question 1 a) Mention one unit of energy, apart from joule, that is used to express the following. [2] b) A ring is melted and made into a sphere. Describe what happens to its centre of gravity. [2] c) Define kgf. How is it related to the SI unit of force? [2] i. Heat energy ii. Electrical energy iii. Energy released on combustion of fat iv. Energy of an electron d) Give an example of a Class 1 lever whose mechanical advantage is lesser than 1. Describe the benefit of the machine named by you. [2] e) The number of teeth on the driver and the follower gear are 36 and 12 respectively. i. What is the use of such a gear train? [1] ii. Justify your answer to the question above. [1] a) A ball is thrown upwards. Explain why the work done by the force of gravity is negative. [2] Question 2 b) A ball is dropped from a height of 4 m. i. What is the maximum height to which the ball can bounce back after hitting the ground? [1] ii. Why is the actual height lesser than the one stated by you above? c) Why is the mechanical advantage of an inclined plane always greater than 1? [1] [2] d) A metal ball is placed upon a compressed spring. Explain why the metal ball accelerates when the spring is released. [2] e) Why is centrifugal force said to be a fictitious force? [2] Question 3 a) A machine displaces a load of 125 kgf through a distance of 0.3 m when an effort of 12.5 kgf acts through a distance of 4 m. Calculate the velocity ratio, mechanical advantage and the efficiency of the machine. [3] b) Two forces of 20 N each act at the 0 cm and 100 cm mark of a metre rule respectively as shown below. 20 N 100 cm 0 cm 20 N i. Calculate the moment produced. ii. A force at the 70 cm mark brings the rule to equilibrium. Determine the magnitude of this force. [1] [2] [2] c) A 1000 kg car races from 10 m.s- 1 to 20 m.s- 1 in 12 seconds. i. Calculate the power output of the car. ii. With the same power, how much time will the car take to go from 20 m.s- 1 to 30 m.s- 1? [2] Question 4 a) A wooden crate of mass 50 kg is to be lifted to a height of 10 m. i. ii. Which of the machines should to be used for this purpose a plank inclined at 30 with horizontal or a single movable pulley? Assume that friction in both is zero. [1] Justify your answer. [2] i. Determine the velocity of the ball at the base of the inclined plane. [2] ii. Why is the actual velocity of the ball lesser than the one calculated? [1] b) A ball is rolled on an inclined plane from a height of 3.6 m. c) A man uses a pulley system of 5 pulleys to lift a load of 3600 N. If the effort applied was 800 N, i. Determine the mechanical advantage of the pulley system. [1] ii. Determine the efficiency of the pulley system. [1] iii. Determine the resistance due to the weight of the movable block and friction. [2] MARKING SCHEME OF MECHANICS TEST Question 1 a) Mention one unit of energy, apart from joule, that is used to express the following. i. Heat energy calorie (cal) ( mark) ii. Electrical energy kilowatt- hour (kWh) ( mark) iii. Energy released on combustion of fat Calorie of (kcal or Cal) ( mark) iv. Energy of an electron electron- volt (eV) ( mark) b) A ring is melted and made into a sphere. Describe what happens to its centre of gravity. [2] [2] The centre of gravity of a ring is outside its mass (1 mark) and at its geometrical centre. When it is melted, and cast into a sphere, centre of gravity comes inside its mass (1 mark) and at its geometrical centre. c) Define kgf. How is it related to the SI unit of force? [2] 1 kgf is the magnitude of the force of the earth s gravity acting on a mass of 1 kg. (1 mark) 1 kgf = 9.8 N (1 mark) d) Give an example of a Class 1 lever whose mechanical advantage is lesser than 1. Describe the benefit of the machine named by you. [2] Scissors (1 mark) Load moves by greater distance, so more length of paper or cloth is cut for same effort (1 mark) e) The number of teeth on the driver and the follower gear are 36 and 12 respectively. i. What is the use of such a gear train? [1] [1] Gain in speed (1 mark) ii. Justify your answer to the question above. VR = 36 / 12 =3, which is greater than 1 (1 mark) Question 2 a) A ball is thrown upwards. Explain why the work done by the force of gravity is negative. [2] W = FScos Since F and S are in the opposite direction, = 180 (1 mark). Hence cos = - 1 (1 mark), and work done is negative b) A ball is dropped from a height of 4 m. i. What is the maximum height to which the ball can bounce back after hitting the ground? [1] 4 m (1 mark) ii. Why is the actual height lesser than the one stated by you above? [1] Some amount of kinetic energy is converted to heat energy ( mark) and sound energy ( mark) c) Why is the mechanical advantage of an inclined plane always greater than 1? [2] In an inclined plane, is always lesser than 90 ( mark). In an inclined plane, MA = 1 / sin ( mark). If < 90 ( mark), sin < 1( mark). Hence MA > 1. d) A metal ball is placed upon a compressed spring. Explain why the metal ball accelerates when the spring is released. [2] [2] The compressed spring has elastic potential energy (1 mark). When released, it does work (1 mark) on the ball. e) Why is centrifugal force said to be a fictitious force? Centrifugal force is said to be a fictitious force since there is no agent (1 mark) pushing or pulling the body experiencing the centrifugal force. The body feels centrifugal force on account of inertia (1 mark). Question 3 a) A machine displaces a load of 125 kgf through a distance of 0.3 m when an effort of 12.5 kgf acts through a distance of 4 m. Calculate the velocity ratio, mechanical advantage and the efficiency of the machine. VR = dE / dL = MA = L / E MA / VR X 100 Efficiency = 4 m / 0.3 cm = 13.33 (1 mark) = 125 kgf / 12.5 kgf = 10 = 10 / 13.33 X 100 = 75 % (1 mark) [3] (1 mark) b) Two forces of 20 N each act at the 0 cm and 100 cm mark of a metre rule respectively as shown below. 20 N 100 cm 0 cm 20 N i. Calculate the moment produced. Moment of the couple ii. = 20N X 1 m = 20 Nm (1 mark) [1] A force at the 70 cm mark brings the rule to equilibrium. Determine the magnitude of this force. force = torque / distance from pivot = 20 Nm / 0.2 m = 100 N (1 mark) (1 mark) [2] c) A 1000 kg car races from 10 m.s- 1 to 20 m.s- 1 in 12 seconds. i. ii. Calculate the power output of the car. Power = work / time = change in energy / time Work = X 1000 (202 - 102) = 150000 J (1 mark) Power = 150000 J / 12 s = 12500 W (1 mark) With the same power, how much time will the car take to go from 20 m.s- 1 to 30 m.s- 1? Time = work / power = change in energy / power Work = X 1000 (302 - 202) = 250000 J (1 mark) Time = 250000 J / 12500 W = 20 s (1 mark) [2] [2] Question 4 a) A wooden crate of mass 50 kg is to be lifted to a height of 10 m. i. Which of the machines should to be used for this purpose a plank inclined at 30 with horizontal or a single movable pulley? Assume that friction in both is zero. [1] [2] (1 mark) Plank (1 mark) ii. Justify your answer. When there is no friction, MA of the plank inclined at 30 is 2 However, even if there is no friction, the actual MA of the single movable pulley is lesser than 2 because of the weight of the movable pulley (1 mark) b) A ball is rolled on an inclined plane from a height of 3.6 m. i. ii. Determine the velocity of the ball at the base of the inclined plane. KE of ball at base = GPE at the top ( mark) mv2 = mgh ( mark) v = 2 ( mark) v = 2 10 3.6 v = ( mark) 8.46 m.s- 1 Why is the actual velocity of the ball lesser than the one calculated? [2] [1] Some kinetic energy is converted into heat energy ( mark) and sound energy ( mark). c) A man uses a pulley system of 5 pulleys to lift a load of 3600 N. If the effort applied was 800 N, i. ii. iii. Determine the mechanical advantage of the pulley system. MA = 3600 N / 800 N ( mark) = 4.5 ( mark) Determine the efficiency of the pulley system. Efficiency = MA / VR X 100 = 4.5 / 5 X 100 ( mark) = 90 % ( mark) Determine the resistance due to the weight of the movable block and friction. MA = n R/E ( mark) R = (n MA) E ( mark) R = (5 4.5) 800 ( mark) = 400 N ( mark) [1] [1] [2]
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