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A Force of 12 N does a work of 12 j on a body when the body is displaced through 2 m . At what angleto the displacement does the force act.
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A Force of 12 N does a work of 12 j on a body when the body is displac...
Work = F S cos theta, where F= force, S= displacement and theta= the angle between force and displacement.
12= 12*2 cos theta
12= 24 cos theta
cos theta = 12/24= 1/2
cos theta = 1/2
cos theta = cos 60degree
theta = 60degree
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A Force of 12 N does a work of 12 j on a body when the body is displac...
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A Force of 12 N does a work of 12 j on a body when the body is displac...
Explanation:
To find the angle at which the force acts, we can use the formula for work:
Work = Force × Distance × cos(θ)
Where:
- Work is the amount of work done (in joules, J)
- Force is the applied force (in newtons, N)
- Distance is the displacement (in meters, m)
- θ is the angle between the force vector and the displacement vector
Given:
- Force = 12 N
- Work = 12 J
- Distance = 2 m
Now, let's substitute these values into the formula and solve for θ:
12 J = 12 N × 2 m × cos(θ)
Simplifying the equation:
1 J = 1 N × 2 m × cos(θ)
Dividing both sides by 2 N m:
0.5 J/N m = cos(θ)
To find the angle θ, we need to take the inverse cosine (cos⁻¹) of both sides:
θ = cos⁻¹(0.5 J/N m)
Using a calculator, we find:
θ ≈ 60.0°
Therefore, the force acts at an angle of approximately 60 degrees to the displacement.
Summary:
- The force of 12 N does a work of 12 J on a body when the body is displaced through 2 m.
- To find the angle at which the force acts, we can use the formula for work.
- Substituting the given values into the formula and solving for θ, we find that the force acts at an angle of approximately 60 degrees to the displacement.
To find the angle at which the force acts, we can use the formula for work:
Work = Force × Distance × cos(θ)
Where:
- Work is the amount of work done (in joules, J)
- Force is the applied force (in newtons, N)
- Distance is the displacement (in meters, m)
- θ is the angle between the force vector and the displacement vector
Given:
- Force = 12 N
- Work = 12 J
- Distance = 2 m
Now, let's substitute these values into the formula and solve for θ:
12 J = 12 N × 2 m × cos(θ)
Simplifying the equation:
1 J = 1 N × 2 m × cos(θ)
Dividing both sides by 2 N m:
0.5 J/N m = cos(θ)
To find the angle θ, we need to take the inverse cosine (cos⁻¹) of both sides:
θ = cos⁻¹(0.5 J/N m)
Using a calculator, we find:
θ ≈ 60.0°
Therefore, the force acts at an angle of approximately 60 degrees to the displacement.
Summary:
- The force of 12 N does a work of 12 J on a body when the body is displaced through 2 m.
- To find the angle at which the force acts, we can use the formula for work.
- Substituting the given values into the formula and solving for θ, we find that the force acts at an angle of approximately 60 degrees to the displacement.
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