Question

A 63.0 kg sprinter starts a race with an acceleration of 4.20 m/s². What is the net external force on him?

Short answer

The net external force is 264.6 N.

Step-by-step solution

Given Data

The given data is listed as below,

• Mass of the sprinter is, $\mathrm{m}$= 63 kg.

• Acceleration is, $\mathrm{a}$= 4.20 m/s2.

Concept of Newton’s second law of motion

Significant Newton’s second law of motion states that the acceleration of a system is directly proportional to the net external force acting on the system and is inversely proportional to the mass of the system. Mathematically,

${\mathrm{F}}_{\mathrm{net}}=\mathrm{ma}$ ………. (i)

Here,

(a).${\mathrm{F}}_{\mathrm{net}}$is the net force

(b). $\mathrm{m}$is the mass

(c).$\mathrm{a}$ is the acceleration.

Determine the net external force acting on the sprinter

Substitute 63 kg for $\mathrm{m}$and 4.20 m/s2 for $\mathrm{a}$ in equation (i),

$$\begin{gathered} {\mathrm{F}}_{\mathrm{net}}=63\mathrm{kg}\times 4.20\mathrm{m}/{\mathrm{s}}^2 \\ =264.6\mathrm{kg}‐\mathrm{m}/{\mathrm{s}}^2 \\ =264.6\mathrm{N} \end{gathered}$$

Hence, the net external force on him is 264.6 N.