# Frank Solutions for Chapter 1.3 Simple Machines Class 10 Physics ICSE

## Exercise

1. What is the use of a fixed pulley?
A fixed pulley is used to change the direction of effort to a convenient direction.

2.  What is an ideal machine?
A machine whose efficiency is 100% is referred to as an ideal machine.

3. Write the relation between mechanical advantage, velocity ratio and efficiency.

4. Can a machine be 100% efficient?
No, a machine cannot be 100% efficient because mechanical advantage is always less than theoretical mechanical advantage due to friction and the weight of the moving parts.

5. Define velocity ratio? State its unit.
Velocity ratio is defined as the ratio of velocity of the effort (VE) to the velocity of the resistance force (load)(VL).
It is also defined as the ratio of the displacement of the effort to the displacement of the load. Mathematically, we have :

Since velocity ratio is the ratio of two similar quantities, therefore, it does not have a unit.

6. What is the purpose of a machine?
The purpose of a machine is:
1. To multiply force
2. To obtain a gain or decrease in speed
3. To change to direction of application of force in a convenient direction

7. Give an example for each of the following uses of a machine: (i) to obtain gain in force,
(ii) to change the point of application of force,
(iii) to change the direction of force,
(iv) to obtain gain in speed.
(i) A jack is used to multiply force.
(ii) A lever is used to change the point of application of force.
(iii) A pulley is used to change the direction of application of force.
(iii) Gears are used to multiply speed.

8. The diagram below shows a pulley arrangement.

(i) In the diagram, mark the direction of the forces due o tension, acting on the pulley P.
(ii) What is the purpose of the pulley Q ?
(iii) If the tension is T newton, deduce the relation between T and E.
(iv) Calculate the velocity ratio of the arrangement.
(v) Assuming that hte efficiency of the system is 100%, what is the mechanical advantage ?
(vi) Calculate the value of E.

(ii) The purpose of the pulley Q is to change the direction of application of effort to a convenient direction.
(iii) In the given diagram, T = E
(iv) If the free end of the string moves, through the distance x, the load will rise by a distance x/2.
Therefore, V.R. = distance moved y the effort arm/distance moved by the load = x(x/2) = 2
(v) In equilibrium, L = 2T and E =T
Efficiency = M.A./V.R.

9. What is a block and tackle system of pulleys?
A block and tackle system of pulleys consists of two blocks of pulleys, each block having one or more than one pulley. The upper block of pulleys is fixed to a rigid support and the lower block of pulleys is movable. The number of pulleys in the movable block is either equal to or one less than the number of pulleys in the fixed block.

10. In which direction will the force be applied when a single pulley is used with a mechanical advantage greater than unity?
When a single pulley is used with a mechanical advantage greater than 1, the effort has to be applied in the upward direction.

11. In a single fixed pulley, If the effort moves by a distance y downwards, by what height is the load raised?
In a single fixed pulley, if the effort moves by a distance 'y' downwards, the load moves by a distance 'y' upwards because the velocity ratio of a single fixed pulley is 1.

12. What is a single movable pulley? What is its mechanical advantage in the ideal case?
A pulley whose axis of rotation is not fixed in position or space is called a movable pulley. Ideally, its M.A. is 2.

13. Name the type of single pulley that can act as a force multiplier. Draw a labeled diagram of the pulley mentioned by you.
Single movable pulley acts as a force multiplier.

14. Give reasons for the following:
(i) In a single fixed pulley, the velocity ratio is always more than the mechanical advantage.
(ii) The efficiency of a pulley is always less than 100%.
(iii) In case of a block and tackle arrangement, the mechanical advantage increases with the increase in the number of pulleys.
(i) In a single fixed pulley, some effort is wasted in overcoming friction between the strings and the grooves of the pulley ; so the effort needed is greater than the load and hence the mechanical advantage is less than the velocity ratio.
(ii) The two reasons are:
• Some effort is wasted n overcoming the friction between the string and the grooves of the pulley.
• Some effort is wasted in lifting up the movable block along with the load.
On account of the above two reasons, the M.A. is always less than the V.R. Hence efficiency is always less than 100%.
(iii) In a block and tackle system, if the total number  of pulleys used in both the blocks is 'n' and the effort is being applied in the downward direction, then the tension in n segments of string supports the load, therefore
L = n T and E = T
M.A. = load/effort = nT/T = n
Thus in a block and tackle system, the M.A. is equal to the number of pulleys and it increases with the increase in the number of pulley.

15. Name a machine which is used to:
(a) multiply force
(b) multiply speed
(c) change the direction of force applied.
(a) A jack is used to multiply force.
(b) Gears are used to multiply speed.
(c) A pulley is used to change the direction of application of force.

16. Write two uses of pulleys. Is pulley a force multiplier?
Two uses of pulley:
• To change the direction of application of force to a convenient direction.
• To multiply force.
Yes, a pulley is a force multiplier

17. In fig. draw a tackle to lift a load by applying the force in a convenient direction. Mark the position of load and effort .

(i) If the load is raised by 1 m, through what distance will the effort move ?
(ii) State how many strands of tackle are supporting the load ?
(iii) What is the mechanical advantage of the system ?
Correct winding of rope around pulleys, load and effort is as shown :

18. Fig. shows a block and tackle system of pulleys used to lift a load.

(i) How many strands of tackle are supporting the load ?
(ii) Draw arrows to represent tension in each stand.
(iii) What is the mechanical advantage of the system ?
(iv) When load is pulled up by a distance 1 m how far does the effort end move ?
(i) 4 strands of tackle are supporting the load.
(ii) Correct winding of rope around pulleys, load and effort is as shown :

19. What is a block and tackle system of pulleys?
A block and tackle system of pulleys consists of two blocks of pulleys, each block having one or more than one pulley. The upper block of pulleys is fixed to a rigid support and the lower block of pulleys is movable. The number of pulleys in the movable block is either equal to or one less than the number of pulleys in the fixed block.

20. Fig. shows a system of four pulleys. The upper two pulleys are fixed and the lower two are movable.

(i) Draw a string around the pulleys. Also show the place and direction in which the effort is applied.
(ii) What is the velocity ratio of the system?
(iii) What is the mechanical advantage of the system ?
(iv) What assumption do you make in arriving at your answer in part (iii) ?