Math Problem Statement

A 62 kg sprinter starts a race with an acceleration of 4.2 m/s2. What is the net external force on him? Express the numeral of your answer in SI units with 3 or more significant figures.

Solution

To find the net external force acting on the sprinter, we can use Newton's second law of motion:

F=maF = m \cdot a

Where:

  • FF is the net external force,
  • mm is the mass of the sprinter, and
  • aa is the acceleration.

Given:

  • m=62kgm = 62 \, \text{kg},
  • a=4.2m/s2a = 4.2 \, \text{m/s}^2.

Now we calculate the force:

F=62kg×4.2m/s2=260.4NF = 62 \, \text{kg} \times 4.2 \, \text{m/s}^2 = 260.4 \, \text{N}

The net external force on the sprinter is 260.4N260.4 \, \text{N}.

Would you like more details or have any questions?

Here are 5 related questions to explore:

  1. How would the net force change if the sprinter’s mass increased by 10%?
  2. What is the sprinter's velocity after 2 seconds, assuming constant acceleration?
  3. How much work is done by the net force over 5 meters?
  4. What is the sprinter’s momentum at a speed of 8 m/s?
  5. How would air resistance affect the net external force?

Tip: Always keep units consistent when solving physics problems to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Newton's Second Law
Force
Acceleration

Formulas

F = m × a

Theorems

Newton's Second Law of Motion

Suitable Grade Level

Grades 9-12