Question

A horizontal force of \[1.2\;{\rm{kg}} \cdot {\rm{wt}}\] is applied to a \[1.5\;{\rm{kg}}\]block resting on a horizontal surface. If \[\mu = 0.3\]. Find the acceleration produced in the block.

Answer 1

Hint: The above problem can be resolved by using the concept and the fundamentals of the frictional force and the net force acting on the horizontal surface. When an object is moving in a horizontal plane, such that there is some friction between the surface and object, then net force is given by taking the difference between horizontal force and frictional force. Then we can substitute the values of gravitational acceleration and other variables like the mass of the block, producing the acceleration of the block.

Complete step by step answer:
Given:
The mass on which the horizontal force is acting is, \[M = 1.2\;{\rm{kg}} \cdot {\rm{wt}}\].
The mass of the block is, \[m = 1.5\;{\rm{kg}}\].
The coefficient of friction is, \[\mu = 0.3\].
The magnitude of horizontal force is given as
\[{F_H} = M \times g\]……………………………………………….. (1)
 Here, g is the gravitational acceleration and its value is \[9.8\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}\].
The magnitude of frictional force is,
\[{F_f} = \mu mg\]…………………………………………… (2)
Now using the equation 1 and 2, the acceleration produced in the block is,
\[\begin{array}{l}
ma = {F_H} - {F_f}\\
a = \dfrac{{{F_H} - {F_f}}}{m}
\end{array}\]
Solve by substituting the values in above equation as,
\[\begin{array}{l}
a = \dfrac{{{F_H} - {F_f}}}{m}\\
\Rightarrow a = \dfrac{{Mg - \mu mg}}{m}\\
\Rightarrow a = \dfrac{{\left( {1.2\;{\rm{kg}} \times 9.8\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}} \right) - \left( {0.3 \times 1.5\;{\rm{kg}} \times 9.8\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}} \right)}}{{1.5\;{\rm{kg}}}}\\
\Rightarrow a = 4.9\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}
\end{array}\]
Therefore, the magnitude of acceleration produced in the block is \[4.9\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}\].

Note:
To resolve the given problem, one must know the fundamentals involved in the analysis of net force acting on the block, while moving along the inclined plane. First of all, it is mandatory to remember the basic formula of the horizontal force acting along the plane, including the analysis of friction over the plane. Moreover, it is also vital to know the technique of identifying the net force utilizing the direction of motion of an object.