Machine Elements Quiz 3

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Questions and Answers

What are the two components of linear acceleration?

  • Normal and tangential acceleration (correct)
  • Linear and non-linear acceleration
  • Angular and radial acceleration
  • Centripetal and centrifugal acceleration

What is acceleration?

  • The product of mass and velocity.
  • The second derivative of displacement and time.
  • The rate of change of velocity with respect to time. (correct)
  • The rate of change of displacement with respect to time.

What is the formula for normal acceleration?

  • $\omega^2R$ (correct)
  • $\frac{dV}{dt}$
  • $R\alpha$
  • $\sqrt{(\frac{d^2x}{dt^2})^2 + (\frac{d^2y}{dt^2})^2}$

What does a vector representing the tangential acceleration of a point look like?

<p>It is perpendicular to the line connecting the point and the point of rotation. (B)</p> Signup and view all the answers

What is the relative acceleration method?

<p>A method based on relative motion to analyze acceleration. (B)</p> Signup and view all the answers

What is the formula for the resultant acceleration?

<p>$\sqrt{(\frac{d^2x}{dt^2})^2 + (\frac{d^2y}{dt^2})^2}$ (C)</p> Signup and view all the answers

What is Coriolis' Law?

<p>A law describing the acceleration of a particle moving along a path that is also in motion. (C)</p> Signup and view all the answers

What is Klein's Construction method used for?

<p>Obtaining velocities (B)</p> Signup and view all the answers

What is the space scale (Ks)?

<p>The number of feet on the machine represented by 1 inch on the drawing. (B)</p> Signup and view all the answers

What is the acceleration scale (Ka)?

<p>The acceleration in fps^2 represented by 1 inch on the drawing. (D)</p> Signup and view all the answers

Flashcards

What is acceleration?

The rate of change of velocity with respect to time. It measures how quickly the velocity of an object is changing.

What are the two components of linear acceleration?

The two components of linear acceleration are normal acceleration and tangential acceleration.

What is normal acceleration?

Normal acceleration is the acceleration towards the center of the circular path. It is also called centripetal acceleration.

What is the formula for normal acceleration?

The formula for normal acceleration is ω²R, where ω is the angular velocity and R is the radius of the circular path.

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What does the vector representing the tangential acceleration of a point look like?

The vector representing tangential acceleration is perpendicular to the line connecting the point and the point of rotation.

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What is the relative acceleration method?

The relative acceleration method is a way to analyze the acceleration of an object based on its relative motion to another object.

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What is the formula for the resultant acceleration?

The formula for resultant acceleration is the square root of the sum of the squares of the normal and tangential acceleration: √(a_n² + a_t² ).

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What is Coriolis' Law?

Coriolis' Law describes the acceleration of a particle moving along a path that is also in motion.

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What is Klein's Construction method used for?

Klein's Construction method is used to obtain the velocities of a mechanism by graphical method.

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What is the space scale (Ks)?

Space Scale (Ks) is the number of feet on the machine represented by 1 inch on the drawing.

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What is the acceleration scale (Ka)?

Acceleration Scale (Ka) is the acceleration in fps² represented by 1 inch on the drawing.

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Boxes are sitting on a conveyor belt moving towards right. The belt reaches full linear speed of 45 fpm in 0.5 sec. Determine the linear acceleration, assuming constant acceleration.

The linear acceleration of the conveyor belt is 90 fpm/s or 1.5 ft/s².

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A high-performance vehicle has a 0-to-60 (mph) time of 8.3 s. Determine the linear acceleration and the distance traveled in reaching 60 mph.

The linear acceleration of the vehicle is 10.6 ft/s² and the distance travelled is 264 ft.

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A wheel rotates 400 revolutions counterclockwise while decelerating from 1100 rpm to 800 rpm. Determine the angular acceleration of the wheel.

The angular acceleration of the wheel is -1.243 rad/s².

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The angular velocity of a shaft is increased with constant acceleration from 1000 rpm to 2500 rpm clockwise in 20 s. Determine the angular acceleration of the shaft.

The angular acceleration of the shaft is 7.85 rad/s².

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Starting from rest, a cam accelerates uniformly to 750 rpm clockwise in 8 s. Determine the angular acceleration of the cam.

The angular acceleration of the cam is 9.82 rad/s².

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Study Notes

Machine Elements Quiz 3

  • Acceleration: The rate of change of displacement with respect to time.
  • Components of Linear Acceleration: Angular and radial, centripetal, and normal, tangential.
  • Normal Acceleration Formula: ω²R
  • Tangential Acceleration Vector: Parallel to the line connecting the point and the point of rotation.
  • Relative Acceleration Method: A method for calculating the acceleration of an object relative to the motion; based on analysis of motion in a vacuum; used only for objects moving in a circular path.
  • Resultant Acceleration Formula: (Ra² + ω²R²)
  • Coriolis' Law: A law describing the acceleration of a particle moving along a path that is also in motion; also a law stating that the acceleration of a particle is proportional to the force applied to it; however it only applies to objects moving at relativistic speeds
  • Klein's Construction Method: used to determine the velocity of a projectile, finding the acceleration, obtaining velocities, and also, calculating the angular velocities.
  • Space Scale (Ks): The velocity in ft/s represented by 1 inch on the drawing; The ratio of the number of feet on the machine represented by 1 inch on the drawing.
  • Acceleration Scale (Ka): The acceleration in ft/s^2 represented by 1 inch on the drawing; The ratio of the angular acceleration to the linear acceleration.
  • Question 11: A conveyor moves boxes at a constant acceleration of 1.5 ft/s² to the right.
  • Question 12: A car accelerates from 0 to 60 mph in 8.3 seconds; linear acceleration = 88 ft/s²; distance = 320 ft.
  • Question 13: A wheel rotates 400 revolutions counterclockwise while decelerating from 1100 rpm to 800 rpm. Angular acceleration = 83.78 rad/s².
  • Question 14: Angular velocity of a shaft increases from 1000 rpm to 2500 rpm clockwise in 20 seconds; angular acceleration = 261.8 rad/s²
  • Question 15: A cam accelerates uniformly to 750 rpm clockwise in 8 seconds from rest; angular acceleration = 261.8 rad/s².

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