Effects of forces on speed and direction Knowledge-Based Study

Study notes

1. What Is a Force?

   A force is a push or a pull acting upon an object as a result of its interaction with another object. Forces are vector quantities, meaning they possess both a magnitude (size) and a direction.

   When analyzing how an object moves, we consider the net force ($F_{\\text{net}}$), which is the vector sum of all individual forces acting on that object:

   • Balanced Forces ($F_{\\text{net}} = 0$): If all forces cancel each other out, the object maintains its state of motion. An object at rest stays at rest, and an object moving at a constant speed in a straight line continues to do so without change.
   • Unbalanced Forces ($F_{\\text{net}} \\neq 0$): When the forces acting on an object do not cancel, an acceleration occurs. This acceleration causes a change in the object's velocity, which can involve a change in speed, a change in direction, or both.

   Changing Speed: Speeding Up and Slowing Down

   Whether a net force causes an object to speed up or slow down depends entirely on the orientation of the force relative to the object's direction of motion (velocity, $v$).

   1. Speeding Up (Acceleration in the Direction of Motion)

   When the net force acts in the same direction as the object's velocity, the speed of the object increases over time.

   • Example: Pressing the accelerator pedal in a car provides a forward driving force that aligns with the car's forward motion, causing it to speed up.

   2. Slowing Down (Opposing Forces)

   When the net force acts in the opposite direction to the object's velocity, the speed of the object decreases over time.

   • Example: Applying the brakes or experiencing kinetic friction exerts a backward force against a forward-moving bicycle, bringing it to a stop.

   Changing Direction: Perpendicular and Angled Forces

   Forces do not only alter how fast an object moves; they can also alter the path along which it travels.

   1. Pure Change in Direction (Perpendicular Forces)

   When a net force acts continuously perpendicular (at a 90° angle) to the direction of motion, the speed of the object remains constant while its direction of travel changes continuously.

   • This type of force is known as a centripetal force, and it causes the object to move along a curved or circular path.
   • Example: The tension in a string when swinging a ball in a horizontal circle continually pulls the ball toward the center, altering its heading without altering its instantaneous speed.

   2. Simultaneous Changes in Speed and Direction

   When a net force acts at an angle that is neither strictly parallel nor strictly perpendicular to the velocity, the force can be resolved into two components:

   • A component along the line of motion that changes the object's speed.
   • A component perpendicular to the line of motion that changes the object's direction.
   • Example: A crosswind hitting a moving sailboat at an acute angle pushes the boat sideways while also increasing or decreasing its forward speed.

   Quick Reference Guide

   The following rules summarize how the orientation of the net force relative to the velocity determines the resulting change in motion:

   • Net force parallel to velocity (same direction): Speed increases; direction remains unchanged.
   • Net force antiparallel to velocity (opposite direction): Speed decreases; direction remains unchanged (until the object stops).
   • Net force perpendicular to velocity: Speed remains constant; direction curves toward the force.
   • Net force at an oblique angle to velocity: Both speed and direction change simultaneously.
   • Net force is zero: Both speed and direction remain completely constant (uniform rectilinear motion).