Question

A flat car is pulled with a constant acceleration $2m/s^2$ . The mass of the block is $50kg$. There is friction between the flat car surface and the block. The wheels of the car are rolling without slipping . Then

• A. tension in the string is $350N$
• B. frictional force is $150N$
• C. acceleration of the block is $4m/s^2$
• D. acceleration of center of the weel is $1m/s^2$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A tension in the string is $350N$
B frictional force is $150N$
C acceleration of the block is $4m/s^2$
D acceleration of center of the weel is $1m/s^2$

As the car moves with an acceleration $a_o$, then the box will move with an acceleration $a=2a_o$

So, $a=4m/s^2$ (given $a_o=2m/s^2$)

Also, as the wheels are rolling without slipping, thus the net acceleration of lowest point must be Zero and that of uppermost point must be $2a_c$.

Thus, $a_o=2a_c⟹a_c=1m/s^2$

Friction force, $F=\mu mg=.3\left(50\right)\left(10\right)=150N$

For block: $ma=T-F$

$50\left(4\right)=T-150⟹T=350N$