6.2. Solved Examples: Introduction to Forces; Newton’s Laws
Example 1
A [latex]1550 \text{ kg}[/latex] car moving at [latex]10 \text{ m/s}[/latex] accelerates to [latex]30 \text{ m/s}[/latex] in [latex]10 \text{ s}[/latex]. What is the net force applied to the car?
Given:
[latex]v_i = 10\,\text{m}/\text{s}[/latex]
[latex]v_f = 30\,\text{m}/\text{s}[/latex]
[latex]t = 10\,\text{s}[/latex]
[latex]m = 1550\,\text{kg}[/latex]
[latex]v_i = 10\,\text{m}/\text{s}[/latex]
[latex]v_f = 30\,\text{m}/\text{s}[/latex]
[latex]t = 10\,\text{s}[/latex]
[latex]m = 1550\,\text{kg}[/latex]
Find:
[latex]\text{F } =\text{ }?[/latex]
[latex]\text{F } =\text{ }?[/latex]
Solution:
- Decide which equation works for the question by examining what is given and what needs to be found.
[latex]F = m \times a[/latex], where [latex]a = {\frac{v_f - v_i}{t}}[/latex]
- Substitute the values for the known quantities to find acceleration, then use the value of the acceleration to find the net force [latex]F[/latex].
[latex]a = {\frac{v_f - v_i}{t}} = {\frac{30 - 10}{10}} = 2.0\,\text{m}/\text{s}^2[/latex][latex]F = m \times a = 1550 \times 2.0 = 3100\,\text{N}[/latex]
Answer:
[latex]F = 3100\,\text{N}[/latex]
