Question

An object of mass $m=5\text{kg}$ is being pulled up a rough inclined plane which is at ${45}^{\circ }$ to the horizontal. The object is pulled at a constant speed of $0.8\text{m/s}$ by a force which acts parallel to the inclined plane. The coefficient of kinetic friction between the object and the plane is $0.2$. Calculate the work done by the force in pulling the block by $0.5\text{m}$. ($g=10{\text{m/s}}^2$)

• A. $21.2\text{J}$
• B. $23.2\text{J}$
• C. Zero
• D. $17.68\text{J}$

Answer 1

The correct option is A $21.2\text{J}$


Given,
${\mu }_k=0.2$
$d=0.5\text{m}$
$f_k={\mu }_k\left(50\cos {45}^{\circ }\right)$
Since block moving with constant speed,net acceleration is zero.
$\Rightarrow$ Net force along plane$=0$
$\Rightarrow F-f_k+50\sin {45}^{\circ }=0$
$\Rightarrow F=f_k+50\sin {45}^{\circ }$
$\Rightarrow F=\mu \times 50\cos {45}^{\circ }+50\sin {45}^{\circ }$
$\Rightarrow F=0.2\times 50\cos {45}^{\circ }+50\sin {45}^{\circ }$
$\Rightarrow F=42.42\text{N}$
$\therefore$ Work done by pulling force $W=F\times d=42.42\times 0.5=21.2\text{J}$