Forces and Newton's Laws
Students apply free-body diagrams and Newton's three laws to explain and predict changes in the motion of objects.
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Defining Force
A force is a push or pull caused by an interaction between objects. Force is a vector, so it has both magnitude and direction. Its SI unit is the newton (N). Forces can be contact forces, such as friction, tension, and the normal force, or noncontact forces, such as gravity. Several forces may act on one object at the same time. Their vector sum is the net force. Forces in opposite directions subtract, while forces in the same direction add. For example, if two students push a cart to the right with 40 N and 25 N while friction acts with 15 N to the left, the net force is 50 N to the right. A nonzero net force changes an object’s velocity by changing its speed, direction, or both.
Free-Body Diagrams
A free-body diagram represents one selected object as a dot or simple box and shows every external force acting on it. First, identify the object and separate it mentally from its surroundings. Next, identify each interaction, draw one arrow for each force, and point the arrow in the force’s direction. Label every arrow, and use longer arrows for larger forces when magnitudes are known. Do not include forces the object exerts on other objects. For a book resting on a level table, Earth pulls downward with gravitational force, while the table pushes upward with a normal force. The arrows are equal in length because the book has zero vertical acceleration. Their vector sum is zero. A free-body diagram should also include coordinate axes chosen to make later calculations clear, especially on ramps or in two-dimensional situations.
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. This resistance to a change in motion is called inertia. Mass measures inertia, so an object with more mass is harder to accelerate. A hockey puck sliding on nearly frictionless ice continues in a straight line at almost constant speed because its net force is nearly zero. It does not need a forward force to keep moving. Earlier explanations associated with Aristotle claimed that continued motion required a continued push. Galileo used observations and experiments with rolling objects to show that friction hides an object’s tendency to maintain motion. Newton later expressed this idea as a general law. This historical change illustrates how scientific explanations improve when new evidence challenges earlier models.
Newton's Second Law
Newton’s second law relates net force, mass, and acceleration: Fnet = ma. Acceleration points in the same direction as the net force. For a fixed mass, a larger net force produces a larger acceleration; for a fixed net force, a larger mass produces a smaller acceleration. The formula can be rearranged to highlight the needed quantity: a = Fnet/m or m = Fnet/a. Suppose a 10 kg cart experiences a 30 N net force to the right. Substituting into a = Fnet/m gives a = 30 N/10 kg = 3 m/s² to the right. To solve a force problem, draw a free-body diagram, choose positive directions, add force components to find the net force, select the correct form of the equation, substitute values with units, and check whether the direction and size of the result are reasonable.
Newton's Third Law
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 forces form an interaction pair. They are the same type of force, but they act on different objects, so they do not cancel on a single free-body diagram. For example, when a skater pushes on a wall, the skater exerts a force on the wall, and the wall exerts an equal, opposite force on the skater. The wall’s force accelerates the skater away from it. If two skaters push each other, each experiences the same force magnitude, but the lower-mass skater has the greater acceleration because a = Fnet/m. Third-law forces are simultaneous; one is not a delayed response to the other.
Friction and Applications
Friction is a contact force that acts parallel to a surface and opposes relative motion or the tendency to slide. Static friction prevents surfaces from sliding and adjusts up to a maximum value. Kinetic friction acts after sliding begins and is often smaller than maximum static friction. In a simple model, kinetic friction is fk = μkFN, where μk is the coefficient of kinetic friction and FN is the normal force. Consider a 5 kg crate pulled right with 20 N while kinetic friction acts left with 8 N. The horizontal net force is 12 N to the right, so a = 12 N/5 kg = 2.4 m/s². Friction is useful in walking, braking, and gripping, but it can also produce unwanted heat and wear. Engineers change surface materials, lubrication, tire tread, and shape to control friction for specific applications.