Forces and Newton's Laws
Students construct and evaluate free-body diagrams to predict how balanced and unbalanced forces affect an object's motion.
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Newton's First Law
Newton’s first law states that an object remains at rest or moves with constant velocity unless a nonzero net external force acts on it. Balanced forces produce zero net force, so they do not change velocity. For example, a hockey puck sliding on nearly frictionless ice continues in a straight line at nearly constant speed. Its downward weight and the ice’s upward normal force balance vertically. Small friction and air resistance eventually slow it. This law developed from Galileo’s studies of motion and challenged the older idea that continuous motion always requires a continuous force. Newton later incorporated inertia into a systematic set of laws. Mass measures an object’s resistance to changes in velocity: a more massive object has greater inertia. Evidence about an object’s velocity before and after forces act can therefore reveal whether the net force was zero.
Free-Body Diagrams
A free-body diagram isolates one object and represents every external force acting on it with a labeled arrow. Begin by identifying the object of interest and drawing it as a dot or simple box. Then identify interactions with Earth, surfaces, ropes, springs, or other objects. Draw each force from the object, with arrow direction showing the force’s direction and arrow length indicating relative magnitude. Choose coordinate axes and resolve angled forces into components when needed. Do not include velocity, acceleration, or forces the object exerts on other objects. For example, a hanging lamp has a downward gravitational force and an upward tension force. If the lamp is motionless, the arrows have equal lengths because the net force is zero. A reliable procedure is to list interactions, draw forces, label them, select axes, and check that no external interaction is missing.
Newton's Second Law
Newton’s second law relates net force, mass, and acceleration: ΣF = ma. Acceleration points in the direction of the net force, not necessarily in the direction of motion. To apply the law, draw a free-body diagram, choose axes, add force components along each axis, and solve the resulting equations. The formula can be rearranged to highlight a desired quantity: a = ΣF/m or m = ΣF/a. For example, suppose a 10-kilogram cart experiences a 40-newton push to the right and 10 newtons of friction to the left. The horizontal net force is 30 newtons to the right, so a = 30 N/10 kg = 3 m/s² to the right. Measured accelerations from repeated trials can provide evidence that acceleration increases with net force and decreases as mass increases.
Action-Reaction Pairs
Newton’s third law states that when object A exerts a force on object B, object B simultaneously exerts an equal-magnitude force in the opposite direction on object A. These action-reaction forces are the same type of interaction but act on different objects, so they never cancel on one free-body diagram. For example, when a swimmer pushes water backward, the water pushes the swimmer forward with an equal force. The forces can produce different accelerations because the swimmer and the affected water may have different masses. To identify a pair, name both objects and reverse the wording: force of the swimmer on the water and force of the water on the swimmer. Weight and normal force on a standing person are not a third-law pair because both act on the same object. Each instead has a separate partner force acting on Earth or the floor.
Friction and Inclined Planes
On an inclined plane, choose axes parallel and perpendicular to the surface. Weight, mg, points vertically downward and can be resolved into mg sin θ parallel to the slope and mg cos θ perpendicular to it. If there is no acceleration perpendicular to the plane, the normal force equals mg cos θ. Friction acts parallel to the surface and opposes actual or impending relative motion. Static friction adjusts up to a maximum of μsN, while kinetic friction has magnitude μkN during sliding. For example, a box sliding down a 30-degree ramp has the downhill component mg sin 30° opposed by uphill kinetic friction. Its net downhill force is mg sin 30° − μkmg cos 30°, and its acceleration is that result divided by m. Careful force measurements and repeated motion trials can test whether this model predicts the box’s acceleration.