Work-Energy Equation and Dynamic Equilibrium Quiz

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Questions and Answers

What is the work done on an object undergoing translational motion?

  • The product of force and velocity
  • The product of torque and displacement
  • The product of force and displacement (correct)
  • The product of mass and acceleration

In dynamic equilibrium, what does translational equilibrium imply?

  • The net force acting on the body is zero (correct)
  • The body is not in motion
  • The body is at rest
  • The body is experiencing angular acceleration

What does rotational equilibrium mean in dynamic equilibrium?

  • The body is experiencing angular acceleration
  • The net torque acting on the body is zero (correct)
  • The body is stationary
  • The body is moving with varying angular velocity

Which condition ensures that a body maintains a constant velocity in dynamic equilibrium?

<p>Net force acting on the body is zero (C)</p> Signup and view all the answers

What does it mean for a body to be in dynamic equilibrium?

<p>Net force and torque acting on it are both zero (D)</p> Signup and view all the answers

How would you describe a body in dynamic equilibrium that is in motion?

<p>Moving with constant velocity with zero forces acting on it (D)</p> Signup and view all the answers

What does Hooke's Law describe?

<p>The relationship between force and displacement in a spring (D)</p> Signup and view all the answers

How is the force exerted by a spring related to its displacement?

<p>Inversely proportional (B)</p> Signup and view all the answers

What does the negative sign in Hooke's Law indicate?

<p>The force is in the opposite direction to displacement (C)</p> Signup and view all the answers

How is work done by a spring related to the square of displacement?

<p>Directly proportional (B)</p> Signup and view all the answers

What type of energy is stored in a spring when work is done on it?

<p>Potential energy (D)</p> Signup and view all the answers

In what context is Varignon's Theorem often applied?

<p>In structural analysis and engineering mechanics (B)</p> Signup and view all the answers

What is the coefficient of restitution defined as?

<p>Ratio of final relative velocity to initial relative velocity after collision (A)</p> Signup and view all the answers

In a direct impact, how are the initial velocities of the two bodies positioned?

<p>Along the line connecting their centers (D)</p> Signup and view all the answers

What is special about a central impact?

<p>The line of impact passes through the center of mass of both bodies (A)</p> Signup and view all the answers

Which type of collision involves an impact at an angle rather than head-on?

<p>Oblique Impact (C)</p> Signup and view all the answers

What does the impulse-momentum equation link together?

<p>Force and change in momentum (A)</p> Signup and view all the answers

What is the range of possible values for the coefficient of restitution?

<p>0 to 1 (D)</p> Signup and view all the answers

In an eccentric impact, where does the line of impact pass through?

<p>At least one body's center of mass (A)</p> Signup and view all the answers

What is true about analyzing oblique impacts?

<p>Both linear and angular components are considered (D)</p> Signup and view all the answers

What defines an oblique impact?

<p>Initial velocities are not directly along the line of impact (D)</p> Signup and view all the answers

What does the work done by a spring measure?

<p>Potential energy stored in the spring (D)</p> Signup and view all the answers

What does the negative sign in the expression F = -kx, based on Hooke's Law, signify?

<p>The force exerted by the spring is in the opposite direction to its displacement. (A)</p> Signup and view all the answers

What is the mathematical expression for the work done by a spring, according to Hooke's Law?

<p>W = -(1/2)kx^2 (B)</p> Signup and view all the answers

When a spring is compressed or stretched, what happens to the work done on it?

<p>The work is stored as potential energy in the spring. (B)</p> Signup and view all the answers

What does the expression W = -(1/2)kx^2 represent for a spring?

<p>The elastic potential energy stored in the spring. (A)</p> Signup and view all the answers

How is Varignon's Theorem helpful in structural analysis and engineering mechanics?

<p>It simplifies calculations involving forces acting on a body. (D)</p> Signup and view all the answers

What concept does Hooke's Law establish regarding the relationship between force and displacement?

<p>Force is inversely proportional to displacement. (D)</p> Signup and view all the answers

What does the work-energy equation for translation involve?

<p>Product of force applied along the direction of motion and displacement (D)</p> Signup and view all the answers

How is dynamic equilibrium defined regarding translational equilibrium?

<p>The net force acting on the body is zero, resulting in constant velocity (B)</p> Signup and view all the answers

What does rotational equilibrium mean in dynamic equilibrium?

<p>The body is not experiencing angular acceleration, remaining at rest or moving with constant angular velocity (C)</p> Signup and view all the answers

What effect does dynamic equilibrium have on the body's velocity?

<p>Maintains constant velocity in both translation and rotation (A)</p> Signup and view all the answers

Which scenario indicates that a body is in dynamic equilibrium?

<p>Maintaining a constant velocity with zero net force and torque (D)</p> Signup and view all the answers

How does translational equilibrium relate to acceleration?

<p>Leads to no acceleration in any direction (D)</p> Signup and view all the answers

What does the coefficient of restitution measure in a collision?

<p>The ratio of final velocity to initial velocity (D)</p> Signup and view all the answers

In an eccentric impact, where does the line of impact pass through?

<p>The center of mass of one of the colliding bodies (C)</p> Signup and view all the answers

What is the fundamental concept behind the impulse-momentum equation?

<p>Conservation of linear momentum (D)</p> Signup and view all the answers

How is a central impact different from an eccentric impact?

<p>Central impacts conserve angular momentum (A)</p> Signup and view all the answers

What distinguishes an oblique impact from a direct impact?

<p>The line of impact differs in orientation (C)</p> Signup and view all the answers

Which equation links the work done by a spring with the energy transferred during deformation?

<p>$W = \frac{1}{2}kx^2$ (B)</p> Signup and view all the answers

What happens to the coefficient of restitution as collisions become more inelastic?

<p>It decreases towards 0 (A)</p> Signup and view all the answers

Why is the line of impact crucial in analyzing collisions?

<p>It affects the direction and outcome of the collision (C)</p> Signup and view all the answers

What does Hooke's Law describe?

<p>The behavior of springs when compressed or stretched (C)</p> Signup and view all the answers

How do oblique impacts differ from direct impacts?

<p>The line of impact orientation differs between oblique and direct impacts (C)</p> Signup and view all the answers

What is the mathematical expression for the force exerted by a spring according to Hooke's Law?

<p>F=-kx (A)</p> Signup and view all the answers

Which formula represents the work done by a force over a displacement?

<p>W=Fdx (A)</p> Signup and view all the answers

What does the negative sign in the expression of work done by a spring indicate?

<p>Direction of the force exerted by the spring (B)</p> Signup and view all the answers

How is the work done by a spring related to the displacement?

<p>$W \propto x^2$ (B)</p> Signup and view all the answers

What does the expression $W=-(1/2)kx^2$ represent in relation to a spring?

<p>Potential energy stored in the spring (D)</p> Signup and view all the answers

Why is Varignon's Theorem valuable in structural analysis and engineering mechanics?

<p>To simplify moment calculations for forces not aligned with axes (C)</p> Signup and view all the answers

What is the work done on an object undergoing translational motion?

<p>$F \cdot d$ (C)</p> Signup and view all the answers

What does dynamic equilibrium of a body involve?

<p>Translational and rotational equilibrium together (A)</p> Signup and view all the answers

How is translational equilibrium mathematically expressed in dynamic equilibrium?

<p>Net force = 0 (A)</p> Signup and view all the answers

What does rotational equilibrium imply in dynamic equilibrium?

<p>No external torques acting on the body (D)</p> Signup and view all the answers

Why doesn't dynamic equilibrium mean that a body is stationary?

<p>Because it can be moving with constant velocity (D)</p> Signup and view all the answers

What is the main outcome of a body being in dynamic equilibrium?

<p>Maintains constant velocity (C)</p> Signup and view all the answers

What does the coefficient of restitution measure in a collision?

<p>The ratio of final relative velocity to initial relative velocity (A)</p> Signup and view all the answers

In which type of collision does the line of impact pass through the center of mass of both colliding bodies?

<p>Central Impact (C)</p> Signup and view all the answers

What is the impulse-momentum equation derived from?

<p>Newton's Second Law (B)</p> Signup and view all the answers

How is eccentric impact defined in collision dynamics?

<p>A collision where one body's center of mass is not on the line of impact (A)</p> Signup and view all the answers

What is the range of values for the coefficient of restitution?

<p>$0$ to $1$ (B)</p> Signup and view all the answers

Which equation represents the impulse-momentum relationship?

<p>$J = \Delta p$ (C)</p> Signup and view all the answers

What is conserved in a central impact?

<p>Angular momentum (C)</p> Signup and view all the answers

How does an oblique impact differ from a direct impact?

<p>The line of impact is inclined relative to initial velocities (A)</p> Signup and view all the answers

What does analyzing eccentric impacts involve, compared to analyzing other types of impacts?

<p>Taking into account moment of inertia and angular momentum (B)</p> Signup and view all the answers

How does work done by a spring relate to its deformation?

<p>Inversely proportional to deformation squared (B)</p> Signup and view all the answers

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