Q4-20 - University Physics with Modern Physics

Question

World-class sprinters can accelerate out of the starting blocks with an acceleration that is nearly horizontal and has magnitude $15m/s^2$ . How much horizontal force must a 55-kg sprinter exert on the starting blocks to produce this acceleration? Which body exerts the force that propels the sprinter: the blocks

or the sprinter herself?

Step-by-Step Solution

Answer

The sprinter must exert a force of 825 N on the starting blocks. The equal and opposite force from the blocks propels the sprinter.

Step 1: Given data

The mass of the sprinter is

 $m=55\text{\hspace{0.17em}kg}$

The required acceleration of the sprinter is

 $a=15{\text{\hspace{0.17em}m/s}}^{\text{2}}$

Step 2: Newton's third law and second law

According to Newton's third law the force exerted by a body on another body is equal and opposite to the force exerted by the second body on the first body, that is

 ${\overrightarrow{F}}_{12}=-{\overrightarrow{F}}_{21}.....\left(1\right)$

  

According to Newton's second law, the force   applied on a body is related to mass   of the body and acceleration   of the body as

 $F=ma.....\left(2\right)$

 

Step 3:Force required for the acceleration of the sprinter

According to equation (1), the sprinter exerts a certain force on the starting blocks and the blocks apply the same force on the sprinter. This force from the blocks propel the sprinter forward. From equation (2), the required force is

 $\begin{array}{c}F=55\text{\hspace{0.17em}kg}\times 15{\text{\hspace{0.17em}m/s}}^{\text{2}}\\ =825\cdot (1\text{\hspace{0.17em}kg}\cdot {\text{m/s}}^2\times \frac{1\text{\hspace{0.17em}N}}{1\text{\hspace{0.17em}kg}\cdot {\text{m/s}}^2})\\ =825\text{\hspace{0.17em}N}\end{array}$

 

Thus, the required force is 825 N and is applied by the blocks.