Force-Velocity Relationship

Examples of Force-Velocity Relationship in the following topics:

• Velocity and Duration of Muscle Contraction

  • The shortening velocity affects the amount of force generated by a muscle.
  • The force-velocity relationship in muscle relates the speed at which a muscle changes length to the force of this contraction and the resultant power output (force x velocity = power).
  • Though they have high velocity, they begin resting before reaching peak force.
  • As velocity increases force and power produced is reduced.
  • Although force increases due to stretching with no velocity, zero power is produced.

• Force of Muscle Contraction

  • The force a muscle generates is dependent on its length and shortening velocity.
  • The force a muscle generates is dependent on the length of the muscle and its shortening velocity.
  • The force-velocity relationship in muscle relates the speed at which a muscle changes length with the force of this contraction and the resultant power output (force x velocity = power).
  • As velocity increases force and therefore power produced is reduced.
  • Although force increases due to stretching with no velocity, zero power is produced.

• Circular Motion

  • The relationship between the gravitational pull on the satellite from the Earth ($g'$) and the velocity of the space shuttle is: $mg'= \frac{mv^{2}}{r}$ where $m$ is the mass of the space shuttle, $v$ is the velocity at which it orbits around the earth, and $r$ is the radius of its orbit.
  • It states that an object will maintain a constant velocity unless a net external force is applied.
  • In uniform circular motion, the force is always perpendicular to the direction of the velocity.
  • Since the direction of the velocity is continuously changing, the direction of the force must be as well.
  • In uniform circular motion, the centripetal force is perpendicular to the velocity.

• Simple Harmonic Motion and Uniform Circular Motion

  • Though the body's speed is constant, its velocity is not constant: velocity (a vector quantity) depends on both the body's speed and its direction of travel.
  • This acceleration is, in turn, produced by a centripetal force—a force in constant magnitude, and directed towards the center.
  • Since velocity v is tangent to the circular path, no two velocities point in the same direction.
  • The next figure shows the basic relationship between uniform circular motion and simple harmonic motion.
  • Describe relationship between the simple harmonic motion and uniform circular motion

• Distribution of Molecular Speeds and Collision Frequency

  • (Velocity is a vector quantity, equal to the speed and direction of a particle) To properly assess the average velocity, average the squares of the velocities and take the square root of that value.
  • With no external forces (e.g. a change in temperature) acting on the system, the total energy remains unchanged.
  • If we assume that all velocity states are equally probable, higher velocity states are favorable because there are greater in quantity.
  • Using the above logic, we can hypothesize the velocity distribution for a given group of particles by plotting the number of molecules whose velocities fall within a series of narrow ranges.
  • Identify the relationship between velocity distributions and temperature and molecular weight of a gas.

• Relationship Between Linear and Rotational Quantitues

  • Here, the velocity of particle is changing - though the motion is "uniform".
  • The velocity (i.e. angular velocity) is indeed constant.
  • This is the first advantage of describing uniform circular motion in terms of angular velocity.
  • Second advantage is that angular velocity conveys the physical sense of the rotation of the particle as against linear velocity, which indicates translational motion.
  • With the relationship of the linear and angular speed/acceleration, we can derive the following four rotational kinematic equations for constant $a$ and $\alpha$:

• Drag

  • The drag force is the resistive force felt by objects moving through fluids and is proportional to the square of the object's speed.
  • Unlike simple friction, the drag force is proportional to some function of the velocity of the object in that fluid.
  • This functionality is complicated and depends upon the shape of the object, its size, its velocity, and the fluid it is in.
  • We can write this relationship mathematically as $F_D \propto v^2$.
  • This video walks through a single scenario of an object experiencing a drag force where the drag force is proportional to the object's velocity.

• A Microscopic View: Drift Speed

  • The drift velocity is the average velocity that a particle achieves due to an electric field.
  • The high speed of electrical signals results from the fact that the force between charges acts rapidly at a distance.
  • It is possible to obtain an expression for the relationship between the current and drift velocity by considering the number of free charges in a segment of wire.
  • When charged particles are forced into this volume of a conductor, an equal number are quickly forced to leave.
  • Relate the drift velocity with the velocity of free charges in conductors

• The Second Law: Force and Acceleration

  • Upon collision, more force is exerted by the larger object, causing the smaller object to bounce off with greater velocity.
  • The laws form the basis for mechanics—they describe the relationship between forces acting on a body, and the motion experienced due to these forces.
  • If an object experiences no net force, its velocity will remain constant.
  • The acceleration is the rate of change in velocity; it is caused only by an external force acting on it.
  • This concept, illustrated below, explains Newton's second law, which emphasizes the importance of force and motion, over velocity alone.

• Constant Velocity Produces a Straight-Line

  • If a charged particle's velocity is parallel to the magnetic field, there is no net force and the particle moves in a straight line.
  • If an object experiences no net force, then its velocity is constant: the object is either at rest (if its velocity is zero), or it moves in a straight line with constant speed (if its velocity is nonzero).
  • If the acceleration is zero, any velocity the particle has will be maintained indefinitely (or until such time as the net force is no longer zero).
  • If the magnetic field and the velocity are parallel (or antiparallel), then sinθ equals zero and there is no force.
  • In the case above the magnetic force is zero because the velocity is parallel to the magnetic field lines.