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Force and Acceleration |
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(Assume g = 10 m/s2 or 10 N/kg unless otherwise stated) 1. A car of mass 1000 kg is accelerating at 2 m/s2. What resultant force acts on the car? If the resistance to the motion is 1000 N, what is the force due to the engine? [Answer: 2000 N, 3000 N] 2. A box of mass 50 kg is pulled up from the hold of a ship with an acceleration of 1 m/s2 by a vertical rope attached to it. Find the tension in the rope. What is the tension in the rope when the box moves up with a uniform velocity of 1 m/s. [Answer: 550 N, 500 N] 3. A lift moves (i) up and (ii) down with an acceleration of 2 m/s2. In each case, calculate the reaction of the floor on a man of mass 50 kg standing in the lift. [Answer: (i) 600 N (ii) 400 N] 4. An astronaut is outside her space capsule in a region where the effect of gravity can be neglected. She uses a gas gun to move herself relative to the capsule. The gas gun fires gas from a muzzle of area 160 mm2 at a speed of 150 m/s. The density of the gas is 800 kg m-3 and the mass of the astronaut, including her space suit, is 130 kg. Calculate (a) the mass of gas leaving the gun per second (b) the acceleration of the astronaut due to the gun, assuming that the change in mass is negligible. [Answer: (a) 0.0192 kg (b) 0.022 m/s2] 5. A light string carrying a small bob of mass 5.0 x 10-2 kg hangs from the roof of a moving vehicle. (a) What can be said about the motion of the vehicle if the string hangs vertically? (b) The vehicle moves in a horizontal straight line from left to right, with a constant acceleration of 2.0 m/s2. (i) Show in sketch the force acting on the bob. (ii) By resolving horizontally and vertically or by scale drawing, determine the angle which the string makes with the vertical. (c) The vehicle moves down an incline making an angle of 30 degree with the horizontal with a constant acceleration of 3.0 m/s2. Determine the angle which the string makes with the vertical. [Answer: (b) (ii) 11.3° (iii) 17.0°] 6. A force of 200 N pulls a sledge of mass 50 kg and overcome a constant frictional force of 40 N. What is the acceleration of the sledge? [Answer: 3.2 m/s2] 7. An object of mass 2.00 kg is attached to the hook of a spring-balance and the balance is suspended vertically from the roof of a lift. What is the reading on the spring-balance when the lift is (i) going up with an acceleration of 0.2 m/s2, (ii) going down with an acceleration of 0.1 m/s2, (iii) ascending with uniform velocity of 0.15 m/s. [Answer: (i) 20.4 N (ii) 19.8 N (iii) 20 N] 8. A car of mass 1000 kg is moving up a hill inclined 30 degree to the horizontal. The total frictional force on the car is 1000 N. Calculate the force due to the engine when the car is (a) accelerating at 2 m/s2 (b) moving with a steady velocity of 15 m/s. [Answer: (a) 8000 N (b) 6000 N]
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