Question

A $5\text{kg}$ block is pushed along a floor by a constant applied force that is horizontal and has a magnitude of $60\text{N}$. The figure given below is the block's speed $v$ versus time $t$ as the block moves along $x$ - axis on the floor. What is the coefficient of kinetic friction between the block and the floor? [Take $g=10{\text{m/s}}^2$]

• A. $0.1$
• B. $0.3$
• C. $0.45$
• D. $0.6$

Answer 1

The correct option is B $0.3$

Given that
Initial velocity of the block $\left(u\right)=5\text{m/s}$
Final velocity of the block $\left(v\right)=50\text{m/s}$
Mass of the block $\left(m\right)=5\text{kg}$


Acceleration of the block is $a=\frac{v-u}{t}$
$\Rightarrow a=\frac{50-5}{5}=9{\text{m/s}}^2$
From FBD of block,
$N=mg=50\text{N}$
& $F-{\mu }_{k}N=ma$
$\Rightarrow {\mu }_k=\frac{F-ma}{N}$
$\Rightarrow {\mu }_k=\frac{60-5\times 9}{5\times 10}$
$\Rightarrow {\mu }_k=0.3$
Hence answer (b) is correct.