Question

A painter of mass $100\text{kg}$ is raising himself and the crate (such an arrangement is called Bosun's chair) on which he stands as shown. When he pulls the rope the force exerted by him on the crate's floor is $450\text{N}$. If the crate weighs $25\text{kg}$ then, find the acceleration of the system and the tension in the rope.

• A. $2{\text{ms}}^{-2},750\text{N}$
• B. $3{\text{ms}}^{-2},500\text{N}$
• C. $4{\text{ms}}^{-2},570\text{N}$
• D. $1{\text{ms}}^{-2},50\text{N}$

Answer 1

The correct option is A $2{\text{ms}}^{-2},750\text{N}$

(For Painter)
$T+F-m_{p}g=m_{p}a......\left(1\right)$
(For crate)
$T-F-m_{c}g=m_{c}a......\left(2\right)$
Subtract (2) from (1), we get
$2F+(m_c-m_p)g=(m_p-m_c)a$
$\Rightarrow 900+(25-100)\left(10\right)=75a$
$\Rightarrow 900-750=75a$
$\Rightarrow a=2{\text{ms}}^{-2},T=750\text{N}$