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For a loaded cantilever beam of uniform cross-section, the bending moment (in N.mm) along the length is M(x) = 5x2+10x, where x is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the cross-section at x =10 mm is ________.
Correct answer is '110'. Can you explain this answer?
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Magnitude of Shear Force at x = 10 mm
Given:
Bending moment along the length of the beam, M(x) = 5x^2 - 10x
To find the magnitude of shear force at x = 10 mm, we can differentiate the bending moment equation with respect to x to obtain the shear force equation.
Differentiating the bending moment equation, we get:
dM(x)/dx = d/dx (5x^2 - 10x)
= 10x - 10
The shear force equation is given by:
V(x) = -dM(x)/dx
Substituting the differentiated equation into the shear force equation, we have:
V(x) = -(10x - 10)
= -10x + 10
To find the magnitude of shear force at x = 10 mm, substitute x = 10 into the shear force equation:
V(10) = -10(10) + 10
= -100 + 10
= -90 N
However, we are interested in the magnitude of the shear force, which is the absolute value of the shear force. So, taking the absolute value, we have:
|V(10)| = |-90|
= 90 N
Therefore, the magnitude of the shear force at x = 10 mm is 90 N.
However, the given correct answer is '110'. It is possible that there may be an error in the given bending moment equation or in the calculation. Double-check the given equation and the calculations to ensure accuracy.
Note: In a cantilever beam, the shear force and bending moment vary along the length of the beam. The shear force is the force that acts parallel to the cross-section of the beam, while the bending moment is the moment that causes the beam to bend. The shear force and bending moment are related to each other through the equilibrium equations. The shear force diagram and bending moment diagram are commonly used to visualize the variation of shear force and bending moment along the length of the beam.
Given:
Bending moment along the length of the beam, M(x) = 5x^2 - 10x
To find the magnitude of shear force at x = 10 mm, we can differentiate the bending moment equation with respect to x to obtain the shear force equation.
Differentiating the bending moment equation, we get:
dM(x)/dx = d/dx (5x^2 - 10x)
= 10x - 10
The shear force equation is given by:
V(x) = -dM(x)/dx
Substituting the differentiated equation into the shear force equation, we have:
V(x) = -(10x - 10)
= -10x + 10
To find the magnitude of shear force at x = 10 mm, substitute x = 10 into the shear force equation:
V(10) = -10(10) + 10
= -100 + 10
= -90 N
However, we are interested in the magnitude of the shear force, which is the absolute value of the shear force. So, taking the absolute value, we have:
|V(10)| = |-90|
= 90 N
Therefore, the magnitude of the shear force at x = 10 mm is 90 N.
However, the given correct answer is '110'. It is possible that there may be an error in the given bending moment equation or in the calculation. Double-check the given equation and the calculations to ensure accuracy.
Note: In a cantilever beam, the shear force and bending moment vary along the length of the beam. The shear force is the force that acts parallel to the cross-section of the beam, while the bending moment is the moment that causes the beam to bend. The shear force and bending moment are related to each other through the equilibrium equations. The shear force diagram and bending moment diagram are commonly used to visualize the variation of shear force and bending moment along the length of the beam.
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For a loaded cantilever beam of uniform cross-section, the bending moment (in N.mm) along the length is M(x) = 5x2+10x, where x is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the cross-section at x =10 mm is ________.Correct answer is '110'. Can you explain this answer?
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