A force is an interaction between two objects or between an object and its environment.
A force is a vector quantity, with magnitude and direction.
Common Types of Forces
Normal Force: When an object pushes on a surface, the surface pushes back on the object perpendicular to the surface. This is a contact force.
Friction Force: This force occurs when a surface resists the sliding of an object and is parallel to the surface. Friction is a contact force.
Tension Force: A pulling force exerted on an object by a rope or cord. This is a contact force.
Weight: The pull of gravity on an object. This is a long-range force.
Magnitudes of Common Forces (Examples)
Sun's gravitational force on the earth: 3.5 × 10^{22} N
Thrust of a space shuttle during launch: 3.1 × 10^7 N
Weight of a large blue whale: 1.9 × 10^6 N
Maximum pulling force of a locomotive: 8.9 × 10^5 N
Weight of a 250-lb linebacker: 1.1 × 10^3 N
Weight of a medium apple: 1 N
Weight of smallest insect eggs: 2 × 10^{-6} N
Electric attraction between the proton and the electron in a hydrogen atom: 8.2 × 10^{-8} N
Weight of a very small bacterium: 1 × 10^{-18} N
Weight of a hydrogen atom: 1.6 × 10^{-26} N
Weight of an electron: 8.9 × 10^{-30} N
Gravitational attraction between the proton and the electron in a hydrogen atom: 3.6 × 10^{-47} N
Force Vectors
Use a vector arrow to indicate the magnitude and direction of the force.
Superposition of Forces
Several forces acting at a point on an object have the same effect as their vector sum acting at the same point.
Decomposing a Force into Component Vectors
Choose perpendicular x and y axes.
Fx and Fy are the components of a force along these axes.
Use trigonometry to find these force components.
Notation for Vector Sum
The vector sum of all the forces on an object is called the resultant of the forces or the net force:
\sum F = F1 + F2 + F3 + … = FR
Superposition of Forces - Example
Force vectors are most easily added using components:
Rx = F{1x} + F{2x} + F{3x} + …
Ry = F{1y} + F{2y} + F{3y} + …
Newton’s First Law
An object at rest tends to stay at rest, and an object in motion tends to stay in uniform motion.
A body acted on by zero net force moves with constant velocity and zero acceleration.
Newton’s First Law (Continued)
If a net force acts, it causes acceleration.
If the net force is zero, there is no acceleration.
Newton’s Second Law
If the net force on an object is not zero, it causes the object to accelerate.
Uniform Circular Motion
An object in uniform circular motion is accelerated toward the center of the circle.
The net force on the object must point toward the center of the circle.
Force and Acceleration
The acceleration of an object is directly proportional to the net force \sum F on the object.
a \propto \sum F
Mass and Acceleration
The acceleration of an object is inversely proportional to the object’s mass if the net force remains fixed.
a \propto \frac{1}{m}
Newton’s Second Law of Motion
The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to the mass of the object.
\sum F = ma
The SI unit for force is the newton (N).
1 N = 1 kg \cdot m/s^2
Example Using Newton's Second Law
A worker applies a constant horizontal force of magnitude 20 N to a box with mass 40 kg resting on a level floor with negligible friction. To find the acceleration of the box:
\sum F = F = 20 N = ma
a = \frac{F}{m} = \frac{20 N}{40 kg} = 0.5 m/s^2
Example Using Newton's Second Law II
A waitress shoves a bottle with mass 0.45 kg to her right along a smooth, level counter. The bottle leaves her hand moving at 2.8 m/s, then slows down as it slides because of a constant friction force exerted on it by the countertop. It slides 1.0 m before coming to rest. To find the magnitude and direction of the friction force:
\sum F = F{net} = Ff = ma = 0.45 kg * (-3.9 m/s^2) = -1.8 N
Systems of Units
SI System: We primarily use this system.
British System: Force is measured in pounds, distance in feet, and mass in slugs.
cgs System: Mass is in grams, distance in centimeters, and force in dynes.
Mass and Weight
The weight of an object (on Earth) is the gravitational force that the Earth exerts on it.
The weight W of an object of mass m is:
W = mg
The value of g depends on altitude.
On other planets, g will have an entirely different value than on Earth.
Example: High Diver
A high diver of mass 70 kg jumps off a board 10 m above the water. If her downward motion is stopped 2 s after she enters the water, what average upward force did the water exert on her?
Find v just before the diver hits the water from the equation vf^2 = vi^2 + 2gy:
v_f = \sqrt{2gy} = \sqrt{2 * 9.8 m/s^2 * 10 m} = 14 m/s (downward)
Find deceleration in the water:
a = \frac{vf - vi}{t} = \frac{0 - (-14 m/s)}{2 s} = 7 m/s^2 (upward)
Find the force from \sum F = ma:
F - mg = ma
F = m(g + a) = 70 kg (9.8 m/s^2 + 7.0 m/s^2) = 1176 N
Newton’s Third Law
If you exert a force on a body, the body always exerts a force (the “reaction”) back upon you.
A force and its reaction force have the same magnitude but opposite directions.
These forces act on different bodies.
Applying Newton’s Third Law: Objects at Rest
An apple rests on a table. Identify the forces that act on it and the action-reaction pairs.
Applying Newton’s Third Law: Objects in Motion
A person pulls on a block across the floor. Identify the action-reaction pairs.
A Paradox?
If an object pulls back on you just as hard as you pull on it, how can it ever accelerate?
Free-Body Diagrams
A free-body diagram is a sketch showing all the forces acting on an object.
Multiple Objects Example
Two blocks of masses m1 = 10 kg and m2 = 7 kg are placed in contact with each other on a frictionless surface. A constant horizontal force F = 12 N is applied to m_1.
a) Find the acceleration of the system.
a = \frac{F}{m1 + m2} = \frac{12 N}{10 kg + 7 kg} = 0.7 m/s^2
b) Find the magnitude of the contact force between the two blocks.
P = m_2 a = 7 kg * 0.7 m/s^2 = 4.9 N