Chapter 4, Problem 62A

To determine

Thedifference in the forces exerted by the male lions and human sprinter on the ground during a race.

Answer to Problem 62A

The differences in the forces exerted by the male lions and sprinter on the ground during the race is $\text{950}\text{N}$ .

Explanation of Solution

Given info:

The acceleration of both the male lions and human sprinters is $a_{\text{lion}}=a_{\text{sprinter}}\text{=10}{\text{m/s}}^2$ .

The weight of the lion is $m_{\text{lion}}=\text{170}\text{kg}$ .

The weight of human sprinter is $m_{\text{sprinter}}=75\text{kg}$ .

Consider the forces exerted by the male lions on the ground is denoted by $F_{\text{lion}}$ .

Consider the forces exerted by the human sprinter on the ground is denoted by $F_{\text{sprinter}}$ .

Formula used:

Newton’s Second Law: The object’s acceleration is equivalent to the sum of the forces acting on the object divided by the object’s mass. That is,

  $\begin{array}{l}a=\frac{F_{\text{net}}}{m}\\ F_{\text{net}}=ma\end{array}$

Calculation:

Both male lions and human sprinter exerts forces on the ground during the race.

Find the forces exerted by the male lions on the ground as follows:

Apply Newton’s Second Law:

  $\begin{array}{c}{F}_{\text{lion}}=m_{\text{lion}}{a}_{\text{lion}}\\ =170\text{kg}\times \text{10}{\text{m/s}}^2\\ =1700\text{kg}\cdot {\text{m/s}}^2\times \frac{1\text{N}}{1\text{kg}\cdot {\text{m/s}}^2}\\ =1700\text{N}\end{array}$

Find the forces exerted by the human sprinters on the ground as follows:

Apply Newton’s Second Law:

  $\begin{array}{c}{F}_{\text{sprinters}}=m_{\text{sprinters}}{a}_{\text{sprinters}}\\ =75\text{kg}\times \text{10}{\text{m/s}}^2\\ =750\text{kg}\cdot {\text{m/s}}^2\times \frac{1\text{N}}{1\text{kg}\cdot {\text{m/s}}^2}\\ =750\text{N}\end{array}$

Find the difference in the forces exerted by the male lions and human sprinter as follows:

  $\begin{array}{c}\text{Difference in forces}=F_{\text{lion}}-F_{\text{sprinters}}\\ =1700\text{N}-750\text{N}\\ =\text{950}\text{N}\end{array}$

Conclusion:

Thus, the differences in the forces exerted by the male lions and human sprinter on the ground during the race is $\text{950}\text{N}$ .