Physics 1A: Newton’s Laws & Force Applications

What is a force?

A force is a push or a pull that can change an object’s motion or shape. In physics we treat a force as a vector — it has both a magnitude (how strong) and a direction (which way it pushes). The SI unit is the newton (N), defined so that one newton is the force required to accelerate a 1-kilogram mass at 1 m/s². In symbols:

1 N = 1 kg · m/s²

Forces come in several everyday flavors: weight (the pull of gravity), normal force (the perpendicular push from a surface), friction (a surface force that resists sliding), tension (the pull along a rope or cable), applied force (an external push or pull like a hand shoving a box), and spring force (F = kx from a compressed or stretched spring). The CBE assumes you can identify which of these are present in a given scenario — so learn to read the picture first, then apply the physics.

Newton’s First Law — the law of inertia

Newton’s first law states: an object at rest stays at rest, and an object in motion continues in motion with constant velocity, unless acted upon by a net external force.

Notice the word net. It is possible for many forces to act on an object without any change in motion — as long as they cancel out to zero. A book resting on a table has weight pulling down and a normal force pushing up; the two are equal in magnitude and opposite in direction, so the net force is zero and the book stays at rest. This is not because "nothing is pushing on it" — plenty of things are — but because the pushes and pulls add up to nothing.

The property that resists a change in motion is called inertia. Inertia depends on mass: a bowling ball has more inertia than a tennis ball, which is why the tennis ball is easier to accelerate or stop.

Common CBE test patterns for the first law:

• A hockey puck slides on frictionless ice at constant velocity. Which of the following is required to keep it moving? Answer: nothing. Absence of a net force is enough. Do not fall for the intuitive-but-wrong "some force keeps it moving" answer.
• A car accelerates forward, and a coffee cup slides backward on the dashboard. Why? The cup’s inertia keeps it (nearly) in place while the car accelerates out from under it. From an outside observer’s frame, the cup barely moved; it was the car that jumped forward.
• Seatbelts, airbags, and headrests all exist because the first law makes a passenger continue in their original motion when the car suddenly stops. Real-world engineering is the first law made mandatory.

Newton’s Second Law — F = ma

The second law is the workhorse of every problem in this lesson. It relates the net force on an object to the acceleration it produces:

F_net = m · a

Read it carefully. F_net is the net force — the vector sum of every force acting on the object. Not any one force. If a 5.0-kg box has a 30 N push to the right and a 12 N friction force to the left, then F_net = 30 − 12 = 18 N to the right, and a = F_net / m = 18 / 5.0 = 3.6 m/s². The CBE distractor pattern here is nearly always the answer you get if you use the applied force alone (6.0 m/s²) or friction alone (2.4 m/s²). Always sum the forces first, then divide by mass.

Three subtleties the second law hides:

• Direction matters. Acceleration always points in the same direction as the net force. If forces cancel exactly, acceleration is zero — even if the individual forces are large.
• Mass ≠ weight. Mass (measured in kg) is how much stuff is in the object. Weight (measured in N) is the force gravity exerts on that mass: W = m · g, with g ≈ 9.8 m/s² on Earth. Your mass on the Moon is the same as on Earth; your weight is about one-sixth. When the CBE asks about weight, they want a force in newtons — do not just give kilograms.
• Rearrange, do not memorize. F = ma, a = F/m, m = F/a — all three forms come from one equation. Solve for whatever is unknown; do not carry three memorized versions.

Newton’s Third Law — action-reaction pairs

Newton’s third law states: for every action force, there is an equal and opposite reaction force acting on a different object.

Here is what most students miss. The two forces in a Newton’s third law pair always act on different objects. If you push a wall with your hand, the wall pushes your hand back with equal force — but the two forces do not cancel, because they act on different things (one on the wall, one on your hand).

Compare with the first law: forces that cancel (weight down, normal force up on the same book) both act on the same object. Those are equilibrium forces, not action-reaction pairs. Do not confuse the two.

Everyday examples:

• Walking. Your foot pushes backward on the ground; the ground pushes forward on your foot with equal magnitude. That forward push is what accelerates you.
• Rocket propulsion. The rocket pushes hot gas downward (or backward); the gas pushes the rocket upward (or forward) with equal magnitude.
• A book on a table. The Earth pulls the book down with weight; the book pulls the Earth up with equal force. (Yes, really — you slightly tug on the whole planet. The planet just does not accelerate visibly because its mass is enormous.)

The CBE will ask questions like: "A hammer strikes a nail with a force of 500 N. What is the force the nail exerts on the hammer?" The answer is 500 N (in the opposite direction). Not zero, not smaller, not "it depends" — exactly equal in magnitude. Even though the nail moves and the hammer barely does, the forces are the same. The accelerations differ because the masses are wildly different (a = F/m).

Free-body diagrams — the tool that catches algebra errors

A free-body diagram is a picture that isolates one object and draws every force acting on it as an arrow. It is the most important pre-algebra skill in this course. Every problem you can solve algebraically, you should be able to solve visually first.

Steps to draw a good free-body diagram:

1. Identify the one object you are analyzing. Circle it if it helps. Everything else in the scene — surfaces, ropes, other objects — will appear only as force arrows on this object.
2. Draw a dot or a small box representing the object. Coordinates are up to you, but choose axes that align with the likely direction of motion (for a ramp problem, tilt your axes to align with the incline).
3. Draw an arrow for every force acting on the object. Label each: W or mg for weight, N for normal, f for friction, T for tension, F_applied for external push, etc.
4. Do not draw forces the object exerts on other things — those belong on their free-body diagrams, not this one.
5. Sum forces along each axis to get F_net,x and F_net,y. Apply Newton’s second law along each axis independently.

A properly drawn free-body diagram tells you the answer half the time before you write down any algebra. If your arrows do not balance in the way you expect, either your diagram is missing a force or your intuition is off — either way, you have caught the error early.

Common force scenarios

Physics Semester A tests a small family of setups over and over. Learn the pattern once and you can decode any variant.

Block on a horizontal surface

Forces on the block: weight down, normal force up, applied force horizontal, friction opposing motion. Because vertical motion is zero, the normal force equals the weight: N = mg. Friction magnitude, once the block is sliding, is f = μN = μmg, where μ is the coefficient of kinetic friction. Along the horizontal, F_net = F_applied − f, and a = F_net / m.

Block on a frictionless incline

Tilt your axes so x runs along the ramp (down the slope is positive) and y runs perpendicular to the ramp. Gravity, which points straight down, decomposes into a component along the ramp (mg·sin θ, pulling the block down the slope) and a component perpendicular to the ramp (mg·cos θ, pressing the block into the surface). The normal force balances the perpendicular component: N = mg·cos θ. Along the ramp, F_net = mg·sin θ, and acceleration is a = g·sin θ. Notice that mass cancels — a frictionless incline accelerates every object at the same rate for a given angle.

Rope pulling a block (tension)

Tension is the pull transmitted through a rope, cable, or string. If we assume the rope is ideal (massless and inextensible), the tension is the same throughout its length. When one object pulls another via a rope, both objects experience a force of magnitude T along the rope’s direction. Newton’s second law applied to one end tells you a; applied to the other end, it tells you T. Consistency between the two is your check.

Two masses connected over a pulley (Atwood machine)

Two masses m₁ and m₂ hang from a string over a frictionless pulley. The heavier mass falls; the lighter rises. Because the string is inextensible, both accelerate at the same magnitude a. Using F = ma on each mass separately gives you two equations in two unknowns (a and T), and the solution is a = (m₁ − m₂)·g / (m₁ + m₂) for the magnitude, with the heavier mass falling. This scenario appears every year on physics CBEs, so the setup is worth memorizing.

Where students lose points

The CBE distractor list on force problems is short and predictable:

• Confusing weight with mass. Answering in kg when the question asks for weight in newtons, or vice versa. Always check units on the final answer.
• Adding forces without checking direction. A 30 N right force plus a 12 N left friction gives a net of 18 N right, not 42 N. Signs first.
• Treating action-reaction pairs as canceling on one object. They act on different objects. If you are drawing both on the same free-body diagram, you have made a mistake.
• Forgetting to decompose gravity on a ramp. The whole "sin θ vs cos θ" confusion goes away if you draw a proper free-body diagram with tilted axes.
• Ignoring friction when it is present. If a surface is not called frictionless, assume friction is there. If the coefficient is given, use it.

Worked example — a two-force block problem

A 4.0-kg block sits on a rough horizontal surface with a coefficient of kinetic friction μ = 0.25. A person pushes it horizontally with a 20 N force. Find the block’s acceleration. Use g = 9.8 m/s².

Step 1 — Draw the free-body diagram (in your head or on paper). Forces on the block: weight mg = 4.0 × 9.8 = 39.2 N down; normal N up; applied 20 N right; friction f left.

Step 2 — Vertical equilibrium. The block does not move vertically, so N = mg = 39.2 N.

Step 3 — Friction magnitude. f = μN = 0.25 × 39.2 = 9.8 N (to the left, opposing motion).

Step 4 — Net horizontal force. F_net = 20 − 9.8 = 10.2 N (to the right).

Step 5 — Acceleration. a = F_net / m = 10.2 / 4.0 = 2.55 m/s² to the right.

If a CBE distractor listed 5.0 m/s² (that would be 20 / 4 — ignoring friction), or 0.5 m/s² (that would be F_net after dividing by mg instead of m), you would recognize the type of mistake immediately.

Check yourself

Before moving to practice questions, confirm you can:

1. State Newton’s three laws in one sentence each.
2. Explain the difference between mass and weight, including units.
3. Draw a free-body diagram for a block sitting on a horizontal surface with a horizontal push and friction present.
4. Explain why the two forces in a Newton’s third law pair do not cancel each other out.
5. Given a block on a frictionless ramp of angle θ, write the acceleration in terms of g and θ without looking.
6. Distinguish equilibrium (forces balance on one object) from action-reaction (forces act on two different objects).

Practice with CBE-style questions

Newton’s laws is one of the highest-yield practice areas on the Physics Semester A CBE — nearly every problem past the first section requires drawing forces and applying F = ma. Work through the practice bank filtered by Newton’s Laws & Force Applications — every question includes a full worked solution and identifies the specific error each distractor represents.

Independent practice content aligned to Texas Essential Knowledge and Skills (TEKS) §112.39(c)(4)(D), (c)(4)(E), (c)(4)(F). Not affiliated with TTU K-12, UT High School, UT-Austin, the Texas Education Agency, or any Credit by Examination administrator. Texas CBE™ does not administer any exam or grant academic credit.