Balanced, Unbalanced Forces, Friction, and Gravity: Seventh Grade Science
Forces govern the equilibrium and acceleration of all matter in the universe, operating as contact forces like friction or field forces like gravity.
The Nature of Force: Contact Versus Field Forces
In physics, a force is defined as any push or pull exerted on an object resulting from its interaction with another object. Forces are vector quantities, possessing both numerical magnitude (measured in Newtons, N) and direction. Physicists categorize forces into two primary classes:
- Contact Forces: Result from direct physical contact between surfaces: applied forces, mechanical tension in ropes, normal support force from surfaces, and friction.
- Non-Contact (Field) Forces: Act across empty space without physical contact: gravity, electrostatic forces between charges, and magnetic fields.
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| BALANCED VERSUS UNBALANCED FORCES |
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| BALANCED FORCES (F_net = 0 N): UNBALANCED FORCES (F_net > 0): |
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| Normal Force (50 N) Normal Force (50 N) |
| ^ ^ |
| | | |
| Friction <--- [Box] ---> Applied Friction <--- [Box] ======> App|
| (20 N) | (20 N) (20 N) | (60 N)|
| v v |
| Gravity Force (50 N) Gravity Force (50 N) |
| |
| Result: F_net = 0 N; Result: F_net = 40 N Right; |
| Velocity is CONSTANT (Rest). Box ACCELERATES to the right! |
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Balanced Versus Unbalanced Forces
The net force (F_net) is the vector sum of all individual forces acting simultaneously on an object:
- Balanced Forces: Occur when opposing forces cancel out, producing a net force of zero (F_net = 0 N). When forces are balanced, an object is in mechanical equilibrium. If at rest, it remains at rest; if in motion, it continues moving at constant velocity. Balanced forces cause zero acceleration.
- Unbalanced Forces: Occur when opposing forces do not cancel out, producing a non-zero net force (F_net > 0 N). Unbalanced forces always cause an object to accelerate in the direction of the net force, changing its speed, its direction, or both.
The Physics of Friction
Friction is a resistive contact force that opposes the relative motion or attempted motion of two surfaces in contact. Friction is caused by microscopic surface roughness: even polished metal surfaces feature jagged microscopic peaks and valleys called asperities. When two surfaces slide against each other, these asperities catch, deform, and form micro-welds that resist sliding.
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| THE FOUR TYPES OF FRICTION |
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| Friction Type | Physical Mechanism | Real-World Example |
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| Static Friction | Opposes the initiation| Pushing a heavy refrigerator |
| | of sliding; strongest | that refuses to budge |
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| Sliding (Kinetic) | Opposes motion between| Sled runners sliding across |
| Friction | sliding surfaces | hard packed snow |
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| Rolling Friction | Resistive force when | Ball bearings or rubber car |
| | round objects roll | tires rolling along asphalt |
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| Fluid Friction | Viscous drag in fluids| Air resistance slowing a falling|
| (Drag) | (liquids and gases) | skydiver's parachute |
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Static friction is always stronger than sliding (kinetic) friction for the same materials because stationary asperities have time to settle deeply into one another. Once sliding begins, the surfaces ride across the tops of the asperities, reducing friction. Rolling friction is roughly 100 to 1,000 times weaker than sliding friction, which is why the wheel was a revolutionary technological invention.
Universal Gravitation: Newton's Gravitational Law
Gravity is an attractive field force that operates between all physical matter in the universe possessing mass. In 1687, Isaac Newton published the Universal Law of Gravitation: every particle of matter attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers: F_gravity = G * (m1 * m2) / r^2, where G is the universal gravitational constant (6.674 x 10^-11 N * m^2 / kg^2), m1 and m2 are masses in kilograms, and r is the distance between their centers in meters.
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| THE INVERSE-SQUARE LAW OF GRAVITY |
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| Distance = 1 r ===> Gravitational Force = 1 F |
| Distance = 2 r ===> Gravitational Force = 1/4 F ((1/2)^2 = 1/4) |
| Distance = 3 r ===> Gravitational Force = 1/9 F ((1/3)^2 = 1/9) |
| Distance = 4 r ===> Gravitational Force = 1/16 F ((1/4)^2 = 1/16) |
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| Doubling distance drops gravity to one-fourth! |
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Mass Versus Weight: A Fundamental Distinction
In science, mass and weight are fundamentally different physical quantities:
- Mass: The intrinsic scalar quantity of matter contained within an object, measured in kilograms (kg). Mass remains constant regardless of location in the universe.
- Weight: The vector downward gravitational force exerted on an object's mass by a planetary body:
Weight = mass * gravitational acceleration (W = m * g). Weight is measured in Newtons (N) and varies depending on local gravitational field strength. On the Moon, where surface gravity is one-sixth that of Earth (g_moon = 1.62 m/s^2), a 60-kilogram astronaut has the exact same mass (60 kg) as on Earth, but weighs only 97.2 Newtons compared to 588 Newtons on Earth.
Exercises and Solutions
Exercise 1: Calculating Net Forces and Free-Body Vector Equilibrium. A 25.0-kilogram wooden crate rests on a warehouse floor. The downward gravitational force acting on the crate is 245.0 Newtons. The floor exerts an equal upward normal support force of 245.0 Newtons. A worker pushes horizontally on the crate with a forward force of 120.0 Newtons, while sliding friction between the crate and floor exerts an opposing horizontal force of 45.0 Newtons. (a) Draw upon free-body vector logic to calculate the net vertical force acting on the crate; (b) Calculate the net horizontal force acting on the crate; (c) Calculate the crate's forward acceleration.
Solution 1: (a) In the vertical axis, the upward normal force (+245.0 N) and the downward gravitational force (-245.0 N) are equal in magnitude and opposite in direction: F_net_vertical = +245.0 N - 245.0 N = 0.0 Newtons. The vertical forces are balanced, meaning the crate experiences zero vertical acceleration and remains on the floor. (b) In the horizontal axis, the applied forward force (+120.0 N) is opposed by sliding friction (-45.0 N): F_net_horizontal = +120.0 N - 45.0 N = +75.0 Newtons in the forward direction. The horizontal forces are unbalanced. (c) Using Newton's Second Law, the horizontal acceleration is: a = F_net / m = 75.0 N / 25.0 kg = 3.0 meters per second squared in the forward direction.
Exercise 2: Evaluating Newton's Universal Law of Gravitation. Two orbital communication satellites, each possessing an identical mass of 2,000 kilograms, orbit Earth separated by a distance of 100 meters. (a) Calculate the gravitational attractive force between the two satellites, using G = 6.674 x 10^-11 N * m^2 / kg^2; (b) If orbital maneuvers increase the separation distance between the satellites to 300 meters, calculate the new gravitational force using the inverse-square law.
Solution 2: (a) Using Newton's Universal Gravitation equation: F_gravity = G * (m1 * m2) / r^2 = (6.674 x 10^-11) * (2,000 * 2,000) / (100)^2 = (6.674 x 10^-11 * 4.0 x 10^6) / 10,000 = (2.6696 x 10^-4) / 10,000 = 2.6696 x 10^-8 Newtons. This gravitational force is tiny, which is why humans do not feel gravitational attraction toward everyday objects. (b) When distance increases from 100 meters to 300 meters, the separation distance triples (3x). According to the inverse-square law, gravitational force is proportional to 1 / r^2. Tripling the distance decreases the gravitational force by a factor of three squared: (3)^2 = 9. Therefore, the new gravitational force is one-ninth (1/9) of the original force: F_new = (2.6696 x 10^-8 N) / 9 = 2.966 x 10^-9 Newtons.