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In an experiment to find the velocity and acceleration of a particular cam rotating at 10 rad/s, the values of displacements and velocities are recorded. The slope of displacement curve at an angle of 'θ' is 1.5 m/s and the slope of velocity curve at the same angle is -0.5 m/s2. The velocity and acceleration of the cam at the instant are respectively?
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In an experiment to find the velocity and acceleration of a particular...
Given Information:
- Angular velocity of the cam, ω = 10 rad/s
- Slope of displacement curve at angle θ, ds/dθ = 1.5 m/s
- Slope of velocity curve at angle θ, dv/dθ = -0.5 m/s²
Calculating Velocity:
To find the velocity of the cam at a particular angle θ, we need to differentiate the displacement equation with respect to time.
Let's assume the displacement equation as s = f(θ).
Differentiating with respect to time, we get ds/dt = df(θ)/dθ * dθ/dt.
Since dθ/dt is the angular velocity ω, the equation becomes ds/dt = ω * df(θ)/dθ.
Given ds/dθ = 1.5 m/s, substituting the value in the equation, we get ds/dt = 10 * 1.5 = 15 m/s.
Therefore, the velocity of the cam at the instant is 15 m/s.
Calculating Acceleration:
To find the acceleration of the cam at a particular angle θ, we need to differentiate the velocity equation with respect to time.
Let's assume the velocity equation as v = g(θ).
Differentiating with respect to time, we get dv/dt = dg(θ)/dθ * dθ/dt.
Since dθ/dt is the angular velocity ω, the equation becomes dv/dt = ω * dg(θ)/dθ.
Given dv/dθ = -0.5 m/s², substituting the value in the equation, we get dv/dt = 10 * (-0.5) = -5 m/s².
Therefore, the acceleration of the cam at the instant is -5 m/s².
Conclusion:
- The velocity of the cam at the instant is 15 m/s.
- The acceleration of the cam at the instant is -5 m/s².
- Angular velocity of the cam, ω = 10 rad/s
- Slope of displacement curve at angle θ, ds/dθ = 1.5 m/s
- Slope of velocity curve at angle θ, dv/dθ = -0.5 m/s²
Calculating Velocity:
To find the velocity of the cam at a particular angle θ, we need to differentiate the displacement equation with respect to time.
Let's assume the displacement equation as s = f(θ).
Differentiating with respect to time, we get ds/dt = df(θ)/dθ * dθ/dt.
Since dθ/dt is the angular velocity ω, the equation becomes ds/dt = ω * df(θ)/dθ.
Given ds/dθ = 1.5 m/s, substituting the value in the equation, we get ds/dt = 10 * 1.5 = 15 m/s.
Therefore, the velocity of the cam at the instant is 15 m/s.
Calculating Acceleration:
To find the acceleration of the cam at a particular angle θ, we need to differentiate the velocity equation with respect to time.
Let's assume the velocity equation as v = g(θ).
Differentiating with respect to time, we get dv/dt = dg(θ)/dθ * dθ/dt.
Since dθ/dt is the angular velocity ω, the equation becomes dv/dt = ω * dg(θ)/dθ.
Given dv/dθ = -0.5 m/s², substituting the value in the equation, we get dv/dt = 10 * (-0.5) = -5 m/s².
Therefore, the acceleration of the cam at the instant is -5 m/s².
Conclusion:
- The velocity of the cam at the instant is 15 m/s.
- The acceleration of the cam at the instant is -5 m/s².
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In an experiment to find the velocity and acceleration of a particular cam rotating at 10 rad/s, the values of displacements and velocities are recorded. The slope of displacement curve at an angle of 'θ' is 1.5 m/s and the slope of velocity curve at the same angle is -0.5 m/s2. The velocity and acceleration of the cam at the instant are respectively?
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In an experiment to find the velocity and acceleration of a particular cam rotating at 10 rad/s, the values of displacements and velocities are recorded. The slope of displacement curve at an angle of 'θ' is 1.5 m/s and the slope of velocity curve at the same angle is -0.5 m/s2. The velocity and acceleration of the cam at the instant are respectively? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In an experiment to find the velocity and acceleration of a particular cam rotating at 10 rad/s, the values of displacements and velocities are recorded. The slope of displacement curve at an angle of 'θ' is 1.5 m/s and the slope of velocity curve at the same angle is -0.5 m/s2. The velocity and acceleration of the cam at the instant are respectively? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an experiment to find the velocity and acceleration of a particular cam rotating at 10 rad/s, the values of displacements and velocities are recorded. The slope of displacement curve at an angle of 'θ' is 1.5 m/s and the slope of velocity curve at the same angle is -0.5 m/s2. The velocity and acceleration of the cam at the instant are respectively?.
In an experiment to find the velocity and acceleration of a particular cam rotating at 10 rad/s, the values of displacements and velocities are recorded. The slope of displacement curve at an angle of 'θ' is 1.5 m/s and the slope of velocity curve at the same angle is -0.5 m/s2. The velocity and acceleration of the cam at the instant are respectively? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In an experiment to find the velocity and acceleration of a particular cam rotating at 10 rad/s, the values of displacements and velocities are recorded. The slope of displacement curve at an angle of 'θ' is 1.5 m/s and the slope of velocity curve at the same angle is -0.5 m/s2. The velocity and acceleration of the cam at the instant are respectively? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an experiment to find the velocity and acceleration of a particular cam rotating at 10 rad/s, the values of displacements and velocities are recorded. The slope of displacement curve at an angle of 'θ' is 1.5 m/s and the slope of velocity curve at the same angle is -0.5 m/s2. The velocity and acceleration of the cam at the instant are respectively?.
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In an experiment to find the velocity and acceleration of a particular cam rotating at 10 rad/s, the values of displacements and velocities are recorded. The slope of displacement curve at an angle of 'θ' is 1.5 m/s and the slope of velocity curve at the same angle is -0.5 m/s2. The velocity and acceleration of the cam at the instant are respectively?, a detailed solution for In an experiment to find the velocity and acceleration of a particular cam rotating at 10 rad/s, the values of displacements and velocities are recorded. The slope of displacement curve at an angle of 'θ' is 1.5 m/s and the slope of velocity curve at the same angle is -0.5 m/s2. The velocity and acceleration of the cam at the instant are respectively? has been provided alongside types of In an experiment to find the velocity and acceleration of a particular cam rotating at 10 rad/s, the values of displacements and velocities are recorded. The slope of displacement curve at an angle of 'θ' is 1.5 m/s and the slope of velocity curve at the same angle is -0.5 m/s2. The velocity and acceleration of the cam at the instant are respectively? theory, EduRev gives you an
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