Chapter 4, Problem 7STP

To determine

To Choose: The correct option.

Answer to Problem 7STP

Option (D)

Explanation of Solution

Given:

Mass of a child, $m_1=45\text{ kg}$

Mass of the tire, $m_2=3.2\text{ kg}$

Formula used:

Newton’s second law:

  $F_{net}=ma$

Where,

  $F_{net}=$ Net force.

  $m=$ Mass.

  $a=$ Acceleration.

Calculation:

Let the tension in the rope be $T$ .

Tension in the rope would be in upward direction while the weight of the child and tire would be in downward direction.

Since, there is no acceleration, therefore net force acting on child and tire would be zero.

i.e.

  $\begin{array}{c}{F}_{net}=0\\ T-m_{1}g-m_{2}g=0\\ T=\left(m_1+m_2\right)g\end{array}$

Plugging in the given values:

  $\begin{array}{c}T=\left(45+3.2\right)\times 9.8\\ =472.36\text{ N}\\ T\text{= 4}\text{.7}\times {\text{10}}^2\text{ N}\end{array}$

Conclusion:

Tension in the rope: $T\text{= 4}\text{.7}\times {\text{10}}^2\text{ N}$