Question

A $6kg$ block is kept over a rough surface with coefficients of friction ${\mu }_s=0.6and{\mu }_4=0.4$ as shown in figure. A time varying force $F=4t$($F$ in $newton$ and $t$ in $second$) is applied on the block as shown. Plot a graph between acceleration of block and time. (Take $g=10m/s^2$)

Answer 1

since force is a function of time, and block is placed on rough horizontal surface, initially static frictional force will act and thus, there will be no acceleration.

When force increases the maximum static frictional force , block will set in motion with kinetic frictional force acting on it.

$Max.staticfrictionalforce=\left(0.6\right)\left(6g\right)$

$=\left(36\right)N$

Since , $F=4t$

therefore, $F=36N$

$4t=36$

$t=9seconds$

therefore, till 9 seconds there will be no motion and block will remain at rest.

after this point, with force as a function of time, block will set into motion with kinetic frictional force acting in opposite direction.

therefore,

$4t-\left(0.4\right)\left(6g\right)=6\left(a\right)$

$a=\left(2/3\right)t-4$ where t > 9 s

$y=\left(m\right)x+c$

Hence , graph of a vs t is :