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This is one of our many quizzes on Simple machines. Click on this to access more such competitive quizzes on Mechanics.

Simple machines Quiz 2

physics

 If we take an example of a lever machine such as a nut sheller, then in which relative position will you find the load of the machine?

 Consider the case of a lever machine of second lever class with respect to its fulcrum, position of effort and load. 

  In case of a nut sheller, the lever machine is of second lever class. In this nut sheller, the fulcrum is placed at one end, position of effort is at other end and the load is placed at the centre. It is shown in the diagram given below. $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/4d4e3fb7-e562-4bf7-aed0-cbfa0e2abac42830281845762477802.png"/>

 If you are provided with the actual mechanical advantage $($AMA$)$ of a machine, you will come across two forces. Out of those two, one force is the effort force. Then, find the relation between actual mechanical advantage $($AMA$)$ and the effort force.

 While considering the actual mechanical advantage you will come across some forces that will reduce the efficiency of the working machine. These forces will be such that they will cancel out each other due to the frictional force within them.

  As opposed to the ideal mechanical advantage, in reality, there are some frictional forces that must be overcome, in addition to the resistance force. These forces are seen in the actual mechanical advantage $\left( \text{AMA} \right)$. This AMA provides for the ratio of the two forces, i.e. resistance force and the effort force. It is given by the relation: $AMA = \dfrac{\text{resistance force}}{\text{effort force}}$ Thus, $AMA \propto \dfrac{1}{\text{effort force}}$

 In the equilibrium, a machine shows the relation between mechanical advantage, velocity ratio and efficiency. Determine the effectiveness of the machine if mechanical advantage is $x$ and velocity ratio is $\dfrac{x}{2}$.

 In the equilibrium, a machine is 100% efficient. Thus, you can think of ideal mechanical advantages while finding the efficiency in terms of M.A and V.R.

 The efficiency of a machine is given by the relation: $ \\ \text{Efficiency}=\dfrac{\text{mechanical advantage(M.A)}}{\text{vertical ratio(V.R)}} \\ $  Given, $M.A=x$ and $V.R=\dfrac{x}{2}$ $ \\ $ On putting the values, we get: $ \\ \text{Efficiency}=\dfrac{x}{\dfrac{x}{2}}=\dfrac{2}{x} \\ $ Thus, the efficiency will be directly proportional to M.A of value $2$, and inversely proportional to the V.R of value $x$.

 Which of the following statements would you consider to be true if the normal force between the load and the inclined plane such as a ramp is directed normal to the surface?

 Assume the case of inclined planes with friction, where there will be presence of frictional forces that in turn will provide you with normal force and the coefficient of static friction.

 When we talk of normal force between the load and the inclined plane, There are some frictional forces that cause friction on the inclined plane. It is referred to as the maximum frictional force, and is given by: ${{F}_{f}}=\mu {{F}_{n}}$ $ \\ $ Where, ${{F}_{n}}$ is the normal force And, $\mu$ is the coefficient of static friction between the two surfaces. $ \\ $ In this given case, we assume the ramp to possess frictional force That in turn produces the normal force.

 A long chisel having length of $270\,cm$ has its fulcrum situated at a width of $90\,cm$ from the load. Calculate the mechanical advantage of the chisel. $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/1771565d-a5eb-47c1-ab72-d180aa566bd01200641782693431789.png"/>

 While finding the mechanical advantage of the chisel, you will come across two parallel forces that will be perpendicular to certain distances that will provide you with the principle of moments. On equating forces with the distances you will get the desired result. 

 By the principle of moments, the mechanical advantage is shown by: $ \\ \Rightarrow \dfrac{F_1}{F_2}=\dfrac{d_2}{d_1}$ $ \\ $ Where, ${F_1}$ and ${F_2}$ are two parallel forces, perpendicular to distance ${d_1}$ and ${d_2}$. $ \\ $ Also, moments of load $=$ moments of efforts about the fulcrum. $ \\ $ As shown in the diagram,we have: $ \\ {F_1}=W,{F_2}=P,{d_1}=90\,cm$ and ${d_2}=({d_2}-{d_1})=(270-90)=180\,cm$ $ \\ $ On putting these values, we get: $ \\ \Rightarrow \dfrac{W}{P}=\dfrac{180}{90}=2 \\ $ Thus, the mechanical advantage of the chisel comes out to be $2$.