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Answer :
Sure! Let's solve this problem step by step.
Step 1: Understanding the Problem
- You have a box with a mass of 215 kg placed on an inclined plane.
- The plane is inclined at an angle of 35° with the horizontal.
- We need to find the component of the box's weight that is parallel to the surface of the incline.
Step 2: Calculate the Weight of the Box
- The weight of the box can be calculated using the formula:
[tex]\[
\text{Weight} = \text{mass} \times g
\][/tex]
where [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex].
- For this box:
[tex]\[
\text{Weight} = 215 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 2108.15 \, \text{N}
\][/tex]
Step 3: Calculate the Parallel Component of the Weight
- The component of the weight parallel to the incline is found using the sine of the angle of the incline:
[tex]\[
\text{Weight}_{\parallel} = \text{Weight} \times \sin(\theta)
\][/tex]
where [tex]\( \theta \)[/tex] is the angle of inclination, 35°.
- First, convert the angle from degrees to radians for calculation:
[tex]\[
\text{Angle in radians} = 35° \times \left( \frac{\pi}{180} \right)
\][/tex]
- Then calculate the parallel component:
[tex]\[
\text{Weight}_{\parallel} = 2108.15 \, \text{N} \times \sin\left(35°\right)
\][/tex]
- Substituting the values, the component of the weight parallel to the incline is approximately:
[tex]\[
\text{Weight}_{\parallel} \approx 1209.76 \, \text{N}
\][/tex]
Thus, the component of the weight parallel to the surface of the incline is approximately 1209.76 N.
Step 1: Understanding the Problem
- You have a box with a mass of 215 kg placed on an inclined plane.
- The plane is inclined at an angle of 35° with the horizontal.
- We need to find the component of the box's weight that is parallel to the surface of the incline.
Step 2: Calculate the Weight of the Box
- The weight of the box can be calculated using the formula:
[tex]\[
\text{Weight} = \text{mass} \times g
\][/tex]
where [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex].
- For this box:
[tex]\[
\text{Weight} = 215 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 2108.15 \, \text{N}
\][/tex]
Step 3: Calculate the Parallel Component of the Weight
- The component of the weight parallel to the incline is found using the sine of the angle of the incline:
[tex]\[
\text{Weight}_{\parallel} = \text{Weight} \times \sin(\theta)
\][/tex]
where [tex]\( \theta \)[/tex] is the angle of inclination, 35°.
- First, convert the angle from degrees to radians for calculation:
[tex]\[
\text{Angle in radians} = 35° \times \left( \frac{\pi}{180} \right)
\][/tex]
- Then calculate the parallel component:
[tex]\[
\text{Weight}_{\parallel} = 2108.15 \, \text{N} \times \sin\left(35°\right)
\][/tex]
- Substituting the values, the component of the weight parallel to the incline is approximately:
[tex]\[
\text{Weight}_{\parallel} \approx 1209.76 \, \text{N}
\][/tex]
Thus, the component of the weight parallel to the surface of the incline is approximately 1209.76 N.
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