Question

A coolie uses a sloping wooden plank of length 2.0 m to push up a drum of mass 100 kg into the truck at a height 1.0 m. What is the mechanical advantage of the sloping plank?
A) 6.
B) 5.
C) 2.
D) 10.

Answer 1

Hint:The mechanical advantage is used to solve this problem. The mechanical advantage is defined as the amplification of the force achieved which is done by using any tool or machine. Mechanical advantage can lower the applied force for any particular work.

Formula used:The formula of the mechanical advantage for the inclined plane is given by,
$ \Rightarrow {\text{Mechanical advantage}} = \dfrac{{{\text{Length of the wooden plank}}}}{{{\text{vertical height of the truck}}}}$

Step by step solution:
Step 1:
We are given that the length of the wooden plank often depicted as l which needs to be fixed in a slope shape is two metre.
The height at which the truck is parked or the height, where the wooden plank is resting, often depicted as h is one metre.
It can be written in mathematical form as,
Length of the sloping wooden plank,
$ \Rightarrow l = 2m$
Height of the parked truck,
$ \Rightarrow h = 1m$

Step 2:
To find the mechanical advantage of the sloping wooden plank, we will be using a formula,
$ \Rightarrow {\text{Mechanical advantage}} = \dfrac{{{\text{Length of the wooden plank}}}}{{{\text{vertical height of the truck}}}}$
Here, the length of the wooden plank is divided by the vertical height. This gave us the mechanical advantage of the sloping wooden plank.
\[ \Rightarrow {\text{Mechanical Advantage}} = \dfrac{l}{h}\]
\[ \Rightarrow {\text{Mechanical Advantage}} = \dfrac{2}{1}\]
\[ \Rightarrow {\text{Mechanical Advantage}} = 2\]
Hence, the mechanical advantage of the sloping wooden plank is 2.

Thus, the option C is the correct answer.

Note:
-The ratio taken between the total load which comprises useful load and load of moving parts of a machine and the applied effort on it is called ideal mechanical advantage.
-Mechanical advantage has no unit and is represented by just a pure number irrespective of the count.