Question

5. (a) A constant horizontal force of 4×10³ N is acting on an object of mass 10×10³ kg on ahorizontal surface. The initial velocity of the object is 8.0 m s-¹.Calculate the final velocityof the object after it has moved 150 m(i) if the horizontal surface is smooth and,(ii) if the horizontal surface is rough and exerts an opposing force of 200 N tothe motion of the object.

Answer 1

Given data:

Constant horizontal force,

`F=4*10^3\text{ N}`

Mass of the object,

`m=10*10^3\text{ kg}`

Initial velocity of the object,

`u=8.0\text{ m/s}`

Distance moved;

`s=150\text{ m}`

Free body diagram when surface is smooth;

The force is given as,

`F=ma`

Here, a is the acceleration of the object.

The expression for the acceleration of the object is given as,

`a=(F)/(m)`

Substituting all known values,

`\begin{gathered} a=\frac{4*10^3\text{ N}}{10*10^3\text{ kg}} \\ =0.4\text{ m/s}^2 \end{gathered}`

From third equation of motion the final velocity is given as,

`v=\sqrt[]{u^2+2as}`

Substituting all known values,

`\begin{gathered} v=\sqrt[]{(8.0\text{ m/s})^2+2*(0.4\text{ m/s}^2)*(150\text{ m})} \\ \approx13.56\text{ m/s} \end{gathered}`

Therefore, the final velocity of object when it moved on smooth surface is 13.56 m/s.

(ii)

When the body is moved on the rough surface. The amount of frictional force acting on the object is,

`f=200\text{ N}`

Free body diagram when the surface is rough:

The net force acting on the body is given as,

`F_(net)=F-f_{}^{}`

Substituting all known values,

`\begin{gathered} F_(net)=(4*10^3\text{ N})-(200\text{ N}) \\ =3800\text{ N} \end{gathered}`

The net force acting on the body is given as,

`F_(net)=ma^(\prime)`

Here, a' is the new acceleration of the object.

The expression of the new acceleration is given as,

`a^(\prime)=(F_(net))/(m)`

Substituting all known values,

`\begin{gathered} a^(\prime)=\frac{3800\text{ N}}{10*10^3\text{ kg}} \\ =0.38\text{ m/s}^2 \end{gathered}`

From third equation of motion new velocity of the object is given as,

`v^(\prime)=\sqrt[]{u^2+2a^(\prime)s}`

Substituting all known values,