Lecture 4 Study Notes: Forces, Work, and Mechanical Advantage

Support Force (Normal Force)

• Definition: A support force, often referred to as a normal force, is a contact force perpendicular to the surface that prevents an object from penetrating that surface. It arises when an object rests on or pushes against a surface.

• Direction: The support force always points perpendicular to the surface and acts away from the surface. For an object resting on a horizontal surface, the support force acts directly upwards, opposing gravity. For an object on an inclined plane, it acts perpendicular to the plane's surface.

Newton's Third Law of Motion

• Statement: Newton's Third Law states that for every action, there is an equal and opposite reaction. This means that if object A exerts a force on object B, then object B simultaneously exerts a force of equal magnitude and opposite direction on object A.

• Force Magnitude and Direction: When one object exerts a force on another, the pushed or impacted object exerts an exactly equal amount of force back on the first object, but in the precisely opposite direction. It's crucial to remember that these forces act on different objects; therefore, they do not cancel each other out.- Example: If you push a wall with a force of $100$ Newtons to the right, the wall simultaneously pushes back on you with a force of $100$ Newtons to the left.

Work in Physics

• Definition: In physics, work is done when a force causes a displacement of an object in the direction of the force. For work to be done, two conditions must be met:

  • A force must be applied to an object.

  • The object must undergo a displacement in the direction of the applied force.

• Calculating Work: The work ($W$) done on an object by a constant force ($F$) is calculated as the product of the magnitude of the force, the magnitude of the displacement ($d$), and the cosine of the angle ($\theta$) between the force and displacement vectors:
  $W = Fd \cos(\theta)$
  If the force and displacement are in the same direction, then $\cos(\theta) = \cos(0^{\circ}) = 1$, so $W = Fd$.

• Positive Work: Positive work is done when the force applied to an object has a component in the same direction as the object's displacement. This typically increases the object's kinetic energy (speed) or potential energy (height).

• Negative Work: Negative work is done when the force applied to an object has a component in the opposite direction to the object's displacement. This typically decreases the object's kinetic energy (slows it down) or potential energy (lowers its height).

Mechanical Advantage

• Definition: Mechanical advantage is a measure of how much a simple machine multiplies the force or distance put into it. It quantifies the ratio of output force to input force.

• Function: Mechanical advantage makes jobs easier by allowing a smaller input force to produce a larger output force (e.g., using a lever to lift a heavy object) or by allowing a force to be applied over a shorter distance to move an object over a longer distance, or vice versa.

Unit of Work

• The SI/metric unit for work is the Joule ($J$). One Joule is defined as the work done when a force of one Newton ($N$) causes a displacement of one meter ($m$) in the direction of the force ($1 J = 1 N \cdot m$).