Vivax Solutions

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Pulleys

  1. The masses of two objects are 8 kg and 2 kg respectively. They are  connected to an light inextensible string that goes over a smooth pulley. If they are released from rest, calculate the acceleration and the tension of the string. What is the significance of the words 'inextensible' and 'light' in your calculations.
  2. The masses of two objects are 6 kg and 2 kg respectively. They are  connected to an light inextensible string that goes over a smooth pulley. Find the acceleration of the system, if they are released from rest. Find the velocity of the system after 4 seconds and the distance travelled during this time.
  3. The masses of two objects are 6 kg and 2 kg respectively. They are  connected to an light inextensible string that goes over a smooth pulley. Find the acceleration of the system, if they are released from rest. Then the larger object hits the floor, after 8 seconds. Describe the subsequent motion of the lighter object. How long will it take to come back to rest, after the heavier one hits the floor?
  4. The masses of two objects that are connected to the ends of a string are 8 kg and 2 kg respectively. The string goes over a smooth pulley. When the object is in motion for 5 seconds, the string is cut. Calculate the time taken by the lighter object to reach the highest point of its motion. Find the distance travelled by the heavier object during this time.
  5. The masses of two objects are 6 kg and 2 kg respectively. They are  connected to an light inextensible string that goes over a smooth pulley. If they are released from rest, calculate the acceleration and the tension of the string. Find the tension of the string that connects the pulley to a ceiling, when the objects are in motion.
  6. Two equal masses of 5 kg are connected to a light inextensible string that goes over a smooth pulley. Someone wants to move the system through a distance of 12 m in 2 seconds. Find out how much of mass must be removed from one side to, add to the other side.
  7. A mass of 4 kg is placed on a rough table. It is connected to a mass of 6 kg by a string that goes over a smooth pulley attached to the edge of the table. The larger mass hangs down freely, just staying in balance. Find the frictional force acting on the lighter object. Then a mass of 4 kg is added to 6 kg. Find the acceleration of the system and the new tension of the string.
  8. A mass of 6 kg is placed in the middle of the surface of a table. It is connected to two strings and they were placed over two smooth pulleys that are in opposite ends of the table. One free end of the string is attached to 8 kg and the other end is attached to 2 kg. When the system is released from rest, find the tension of each string and the acceleration.
  9. The length of a table is 2 m and a smooth pulley is attached to one of its edges. An object of mass 4 kg is placed at the opposite end and connected to a string that goes over the pulley. The free end of the string is attached to another object of m kg. When the system is released from rest, they first object reaches the other end in 4 seconds. Assuming that the table is smooth, calculate m.
  10. At the vertex of a triangular wedge lies a smooth  pulley, firmly fitted against the frame. Over the pulley lies a string that is attached to two masses of 6 kg and 4 kg. If the system is in balance, calculate the tension of the strings. The two planes of the wedge make angles 300 and 600 respectively with the horizontal. If they are at the same vertical level, which one would reach the bottom first, if the string is cut?
  11. Two masses of 3 kg and 4 kg are attached to a string. They were taken to a cliff and dropped with the string being slack. Ignoring the air resistance, calculate the tension of the string.
  12. Two masses of 2 kg and 5 kg are attached to a vertical string that remains taut. They were taken to a rooftop and dropped. Find the tension of the string. The air resistance is proportional to the mass of each object. Find an expression for the tension of the strings.
  13. A ball is dropped from an aeroplane. It gathers speed as it comes down and then reaches a constant speed. Explain this. Then draw a distance-time graph to illustrate this.
  14. A ball is attached to the bottom of a pool by a string to stop it from floating. The tension of the string has been found out to be 12 N. The mass of the ball is 3 kg. Find the initial acceleration of the ball, when the string is cut. If the depth of the pool is 2 m, Find the highest point reached by the ball, after leaving water.
  15. A closed box is attached to a string and slowly immersed in water. The tension of the string seems to be in decline at first and then becomes constant. Explain this. What would happen if the box opens up while in water? Will the tension go up or down?