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Five forces acting on a particle the magnitude of force are 300N, 600N, 700N, 900N, and p and their angle are 0*, 60*, 135*, 120*, and 270* with respect to horizontal axis. If the vertical component of all forces is 1000N find the value of p. calculare mag and direction of resultant assuming that the 1st force acts towardd the point, while all the remaining forces act away from the point.?
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Five forces acting on a particle the magnitude of force are 300N, 600N...
**Given:**
- Magnitude of forces: 300N, 600N, 700N, 900N, and p
- Angles of forces with respect to horizontal axis: 0*, 60*, 135*, 120*, and 270*
- Vertical component of all forces: 1000N
**To find:**
- Value of p
- Magnitude and direction of resultant assuming that the 1st force acts towards the point, while all the remaining forces act away from the point.
**Solution:**
***Finding the value of p:***
- Since the vertical component of all forces is 1000N, we can use the trigonometric ratio of sine to find the value of p.
- sin(0*) = 0, sin(60*) = √3/2, sin(135*) = -√2/2, sin(120*) = -√3/2, sin(270*) = -1
- Therefore, the vertical components of the forces are: 0N, 300√3 N, -700√2/2 N, -450√3/2 N, and -1000N respectively.
- The sum of the vertical components of all forces is: 0 + 300√3 - 700√2/2 - 450√3/2 - 1000 = -154.94 N
- Since the sum of all vertical components is equal to 1000N, we can equate them to find the value of p.
- 1000 = 154.94 + p
- Therefore, p = 845.06 N
***Finding the magnitude and direction of resultant:***
- To find the magnitude of resultant, we can use the Pythagorean theorem.
- R^2 = (300)^2 + (600)^2 + (700)^2 + (900)^2 + (845.06)^2 - 2(300)(600)cos(60*) - 2(300)(700)cos(135*) - 2(300)(900)cos(120*) - 2(600)(700)cos(120*) - 2(600)(900)cos(270*) - 2(700)(900)cos(135*)
- R^2 = 630071.57
- R = √630071.57 = 794.43 N
- To find the direction of resultant, we can use the trigonometric ratio of tangent.
- tanθ = ΣFy/ΣFx
- ΣFx = (300) + (600)cos(60*) + (700)cos(135*) + (900)cos(120*) - (845.06)
- ΣFx = 276.57 N
- Therefore, tanθ = (-154.94)/276.57
- θ = -29.89*
- Since the 1st force acts towards the point, while all the remaining forces act away from the point, the direction of resultant is in the opposite direction to the 1st force.
- Therefore, the direction of resultant is 180 - 29.89 = 150.11* with respect to the horizontal axis.
**Answer:**
- Value of p = 845.06 N
- Magnitude of resultant = 794
- Magnitude of forces: 300N, 600N, 700N, 900N, and p
- Angles of forces with respect to horizontal axis: 0*, 60*, 135*, 120*, and 270*
- Vertical component of all forces: 1000N
**To find:**
- Value of p
- Magnitude and direction of resultant assuming that the 1st force acts towards the point, while all the remaining forces act away from the point.
**Solution:**
***Finding the value of p:***
- Since the vertical component of all forces is 1000N, we can use the trigonometric ratio of sine to find the value of p.
- sin(0*) = 0, sin(60*) = √3/2, sin(135*) = -√2/2, sin(120*) = -√3/2, sin(270*) = -1
- Therefore, the vertical components of the forces are: 0N, 300√3 N, -700√2/2 N, -450√3/2 N, and -1000N respectively.
- The sum of the vertical components of all forces is: 0 + 300√3 - 700√2/2 - 450√3/2 - 1000 = -154.94 N
- Since the sum of all vertical components is equal to 1000N, we can equate them to find the value of p.
- 1000 = 154.94 + p
- Therefore, p = 845.06 N
***Finding the magnitude and direction of resultant:***
- To find the magnitude of resultant, we can use the Pythagorean theorem.
- R^2 = (300)^2 + (600)^2 + (700)^2 + (900)^2 + (845.06)^2 - 2(300)(600)cos(60*) - 2(300)(700)cos(135*) - 2(300)(900)cos(120*) - 2(600)(700)cos(120*) - 2(600)(900)cos(270*) - 2(700)(900)cos(135*)
- R^2 = 630071.57
- R = √630071.57 = 794.43 N
- To find the direction of resultant, we can use the trigonometric ratio of tangent.
- tanθ = ΣFy/ΣFx
- ΣFx = (300) + (600)cos(60*) + (700)cos(135*) + (900)cos(120*) - (845.06)
- ΣFx = 276.57 N
- Therefore, tanθ = (-154.94)/276.57
- θ = -29.89*
- Since the 1st force acts towards the point, while all the remaining forces act away from the point, the direction of resultant is in the opposite direction to the 1st force.
- Therefore, the direction of resultant is 180 - 29.89 = 150.11* with respect to the horizontal axis.
**Answer:**
- Value of p = 845.06 N
- Magnitude of resultant = 794
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Five forces acting on a particle the magnitude of force are 300N, 600N, 700N, 900N, and p and their angle are 0*, 60*, 135*, 120*, and 270* with respect to horizontal axis. If the vertical component of all forces is 1000N find the value of p. calculare mag and direction of resultant assuming that the 1st force acts towardd the point, while all the remaining forces act away from the point.?
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Five forces acting on a particle the magnitude of force are 300N, 600N, 700N, 900N, and p and their angle are 0*, 60*, 135*, 120*, and 270* with respect to horizontal axis. If the vertical component of all forces is 1000N find the value of p. calculare mag and direction of resultant assuming that the 1st force acts towardd the point, while all the remaining forces act away from the point.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Five forces acting on a particle the magnitude of force are 300N, 600N, 700N, 900N, and p and their angle are 0*, 60*, 135*, 120*, and 270* with respect to horizontal axis. If the vertical component of all forces is 1000N find the value of p. calculare mag and direction of resultant assuming that the 1st force acts towardd the point, while all the remaining forces act away from the point.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five forces acting on a particle the magnitude of force are 300N, 600N, 700N, 900N, and p and their angle are 0*, 60*, 135*, 120*, and 270* with respect to horizontal axis. If the vertical component of all forces is 1000N find the value of p. calculare mag and direction of resultant assuming that the 1st force acts towardd the point, while all the remaining forces act away from the point.?.
Five forces acting on a particle the magnitude of force are 300N, 600N, 700N, 900N, and p and their angle are 0*, 60*, 135*, 120*, and 270* with respect to horizontal axis. If the vertical component of all forces is 1000N find the value of p. calculare mag and direction of resultant assuming that the 1st force acts towardd the point, while all the remaining forces act away from the point.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Five forces acting on a particle the magnitude of force are 300N, 600N, 700N, 900N, and p and their angle are 0*, 60*, 135*, 120*, and 270* with respect to horizontal axis. If the vertical component of all forces is 1000N find the value of p. calculare mag and direction of resultant assuming that the 1st force acts towardd the point, while all the remaining forces act away from the point.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five forces acting on a particle the magnitude of force are 300N, 600N, 700N, 900N, and p and their angle are 0*, 60*, 135*, 120*, and 270* with respect to horizontal axis. If the vertical component of all forces is 1000N find the value of p. calculare mag and direction of resultant assuming that the 1st force acts towardd the point, while all the remaining forces act away from the point.?.
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Five forces acting on a particle the magnitude of force are 300N, 600N, 700N, 900N, and p and their angle are 0*, 60*, 135*, 120*, and 270* with respect to horizontal axis. If the vertical component of all forces is 1000N find the value of p. calculare mag and direction of resultant assuming that the 1st force acts towardd the point, while all the remaining forces act away from the point.?, a detailed solution for Five forces acting on a particle the magnitude of force are 300N, 600N, 700N, 900N, and p and their angle are 0*, 60*, 135*, 120*, and 270* with respect to horizontal axis. If the vertical component of all forces is 1000N find the value of p. calculare mag and direction of resultant assuming that the 1st force acts towardd the point, while all the remaining forces act away from the point.? has been provided alongside types of Five forces acting on a particle the magnitude of force are 300N, 600N, 700N, 900N, and p and their angle are 0*, 60*, 135*, 120*, and 270* with respect to horizontal axis. If the vertical component of all forces is 1000N find the value of p. calculare mag and direction of resultant assuming that the 1st force acts towardd the point, while all the remaining forces act away from the point.? theory, EduRev gives you an
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