Answered

Rewrite the following expression so that it is easier to read.
Fix any grammar or spelling errors.
Do not remove or change LaTeX formatting.
Do not change or remove [tex] [/tex] tags.
If the expression is nonsense, rewrite it so that it makes sense.
-----

[tex]\[ 9.8 \sin 30^{\circ} - 0.30 \left(9.8 \, \frac{m}{s^2}\right) \cos \theta \][/tex]



Answer :

GinnyAnswer
Let's solve the problem step-by-step.

1. Identify the given values:
- The acceleration due to gravity, [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
- The angle, [tex]\( \theta = 30^\circ \)[/tex]
- The coefficient of friction, [tex]\( \mu = 0.30 \)[/tex]

2. Convert the angle from degrees to radians:
[tex]\[ \theta_{\text{rad}} = 30^\circ \times \frac{\pi}{180^\circ} = \frac{\pi}{6} \, \text{radians} \][/tex]

3. Calculate the sine and cosine of the angle:
[tex]\[ \sin(30^\circ) = \frac{1}{2} \][/tex]
[tex]\[ \cos(30^\circ) = \frac{\sqrt{3}}{2} \][/tex]

4. Compute the components separately:

- Sin component:
[tex]\[ g \sin(30^\circ) = 9.8 \times \frac{1}{2} = 4.9 \, \text{m/s}^2 \][/tex]

- Cos component:
[tex]\[ \mu g \cos(30^\circ) = 0.30 \times 9.8 \times \frac{\sqrt{3}}{2} \approx 0.3 \times 9.8 \times 0.866 = 2.5461 \, \text{m/s}^2 \][/tex]

5. Subtract the cosine component from the sine component:
[tex]\[ 4.9 - 2.5461 \approx 2.3539 \, \text{m/s}^2 \][/tex]

Thus, the final results are:
- The sine component: [tex]\( 4.9 \, \text{m/s}^2 \)[/tex]
- The cosine component: [tex]\( 2.5461 \, \text{m/s}^2 \)[/tex]
- The resulting value after subtraction: [tex]\( 2.3539 \, \text{m/s}^2 \)[/tex]

So, the steps clearly show how we arrive at the final values.

Other Questions