Q4-17E - University Physics with Modern Physics

Question

Superman throws a 2400-N boulder at an adversary. What horizontal force must Superman apply to the boulder to give it a horizontal acceleration of  $12{\text{\hspace{0.17em}m/s}}^{\text{2}}$?

Step-by-Step Solution

Answer

Superman has to apply a horizontal force of 2938.8 N to produce an acceleration of  $12{\text{\hspace{0.17em}m/s}}^{\text{2}}$ on the 2400 N boulder.

Step 1: Given data

The weight of the boulder is,  $W=2400\text{\hspace{0.17em}N}$

The acceleration due to gravity on Earth is   $g=9.8{\text{\hspace{0.17em}m/s}}^{\text{2}}$

The required acceleration of the boulder is   $a=12{\text{\hspace{0.17em}m/s}}^{\text{2}}$

Step 2: Gravitational force and second law of motion

 

The downward gravitational force on a body of mass $m$   is

                $F_g=mg$                                                                                                       …(1)

 

The second law of motion relates the net force $F$ , mass  $m$ and acceleration   as

                         $F=ma$                                                                                                …(2)

Step 3: Force applied by Superman

From equation (1), the mass of the boulder is

  $\begin{array}{c}m=\frac{W}{g}\\ =\frac{2400\text{\hspace{0.17em}N}}{9.8{\text{\hspace{0.17em}m/s}}^{\text{2}}}\\ =244.9\times \left(\frac{1}{{\text{m/s}}^{\text{2}}}\right)\times \left(1\text{\hspace{0.17em}N}\times \frac{1{\text{\hspace{0.17em}kg.m/s}}^{\text{2}}}{1\text{\hspace{0.17em}N}}\right)\\ =244.9\text{\hspace{0.17em}kg}\end{array}$

From equation (2), the force applied to get the required acceleration is

 $\begin{array}{c}F=ma\\ =244.9\text{\hspace{0.17em}kg}\times 12{\text{\hspace{0.17em}m/s}}^{\text{2}}\\ =2938.8\times \left(1{\text{\hspace{0.17em}kg.m/s}}^{\text{2}}\times \frac{1\text{\hspace{0.17em}N}}{1{\text{\hspace{0.17em}kg.m/s}}^{\text{2}}}\right)\\ =2938.8\text{\hspace{0.17em}N}\end{array}$

 

Thus, the required force is 2938.8 N.