FULL REVIEW
Full Review: Newton's Laws and Free-Body Diagrams
Use free-body diagrams, vector components, Newton's laws, friction, tension, and connected-system algebra to solve college-physics force problems.
TIME
45–60 minutes
BEST FOR
A complete topic review
FINISH WITH
A readiness check
After this full review, you'll be able to...
construct complete free-body diagrams, resolve forces into components, and solve Newton's-law problems with friction, tension, and connected objects.
Choose how you want to review
Unit Alignment
This bundle is aligned to the approved Physics Sensei unit specification below. Use it to recover the unit structure, reinforce key decisions, and confirm readiness for the next study task.
ARCHITECTURE: Physics Sensei Independent Mechanics
UNIT: MEC-U05 — Newton's Laws and Free-Body Diagrams
SCOPE: Unit Review
PHYSICS LEVEL: Algebra-Based
BEST USED
✓ Before force-and-friction homework
✓ When component equations are the main challenge
✓ Before a quiz on Newton's laws and FBDs
Your Review Plan
Complete these six stages in order. Each stage builds on the previous one and prepares you for the final readiness check.
6 Stages • Approximately 45–60 minutes.
Warm-Up Check
Before you begin, take a moment to see what you already remember. Do not worry about getting everything right. This is only a starting point.
ACTIVITY 1
Recall Activity
List only forces acting on the chosen object.
A crate is pulled across a rough horizontal floor by a rope angled upward. Which forces belong on the crate's free-body diagram?
Reveal Answers
Weight, normal force, rope tension, and friction.
Why it works: All four are external interactions on the crate. The crate's velocity or acceleration is not itself a force.
ACTIVITY 2
Recall Activity
Translate the diagram into vector equations.
For a system accelerating horizontally with no vertical acceleration, what equations connect the force components to acceleration?
Reveal Answers
ΣFₓ = maₓ and ΣFᵧ = 0.
Why it works: Newton's second law is applied component by component. Zero vertical acceleration makes the vertical force sum zero even while horizontal acceleration is nonzero.
ACTIVITY 3
Recall Activity
Do not pair forces that act on the same object.
A block rests on a table. Is the block's weight the Newton's-third-law partner of the table's normal force?
Reveal Answers
No.
Why it works: Weight and normal both act on the block. Their third-law partners act on Earth and on the table, respectively.
Ready to strengthen your understanding?
You've refreshed what you already know. Next, you'll reinforce the essential concepts that will help you solve problems with confidence. Need to see the learning path again?
Core Concepts
Let's rebuild the key ideas one step at a time. Focus on understanding the relationships before worrying about solving problems.
KEY CONCEPT 1
Resolve forces before solving
After choosing axes, resolve angled forces into components and write one Newton-second-law equation per axis. Signs come from the chosen axes, not from memorized formulas.
EXAMPLE For a pull T at angle θ above horizontal: Tₓ = T cosθ and Tᵧ = T sinθ. If vertical acceleration is zero, N + T sinθ - mg = 0.
SENSEI NOTE An angled pull changes the normal force, which can change friction. Solve the normal direction before substituting f = μN when that model applies.
KEY CONCEPT 2
Use force models with their conditions
Weight is mg near Earth; an ideal rope transmits one tension; kinetic friction has magnitude μₖN and opposes sliding; static friction adjusts up to μₛN.
EXAMPLE Static friction is fₛ ≤ μₛN, not always fₛ = μₛN. Equality applies only at impending slip.
SENSEI NOTE Write the inequality for static friction before assuming the limiting value.
KEY CONCEPT 3
Connected systems share constraints
For connected objects, each object has its own free-body diagram. A massless inextensible rope gives linked accelerations, and internal tensions cancel if the connected objects are treated as one larger system.
EXAMPLE For two blocks of total mass 10 kg pulled by 30 N on a frictionless floor, the system acceleration is 3.0 m/s². Use one block afterward to find tension.
SENSEI NOTE System-level equations often find acceleration fastest; individual-object equations then recover internal forces such as tension.
Ready to apply these ideas?
You've reinforced the essential concepts. Now it's time to put them into practice by working through guided examples and building your problem-solving confidence. Need a quick reminder?
Guided Practice
Now it's time to apply what you've reviewed.
Work through each activity in order. The examples become gradually more challenging, and each one prepares you for the final readiness check.
PRACTICE 1
Worked Example
Resolve the angled pull and update the normal force first.
A 12 kg crate is pulled with 50 N at 30° above horizontal across a floor with μₖ = 0.20. Find its acceleration. Use g = 9.8 m/s².
Reveal Answers
2.06 m/s² horizontally in the pull direction.
Why it works: N = mg - 50 sin30° = 117.6 - 25 = 92.6 N. Then fₖ = 0.20(92.6) = 18.52 N and Tₓ = 50 cos30° = 43.30 N. Thus F_net,x = 24.78 N and a = 24.78/12 = 2.065 m/s².
PRACTICE 2
Guided Problem
Use the whole system for acceleration, then one block for tension.
Blocks of 4.0 kg and 6.0 kg are connected on a frictionless horizontal surface. A 30 N horizontal force pulls the 6.0 kg block. Find the acceleration and the tension.
Reveal Answers
a = 3.0 m/s²; T = 12 N.
Why it works: For both blocks, a = 30/(4+6) = 3.0 m/s². For the 4.0 kg block alone, the only horizontal force is tension, so T = (4.0)(3.0) = 12 N.
PRACTICE 3
Independent Problem
Resolve gravity along and perpendicular to an incline.
A 5.0 kg block slides down a 25° incline with μₖ = 0.15. Find its acceleration down the incline. Use g = 9.8 m/s².
Reveal Answers
2.81 m/s² down the incline.
Why it works: mg sin25° = 20.71 N down the slope; N = mg cos25° = 44.41 N; fₖ = 6.66 N up the slope. Net = 14.05 N down, so a = 14.05/5.0 = 2.81 m/s².
Ready to check your understanding?
You've practiced the essential skills with guidance. Now it's time to solve a few short problems on your own and confirm you're ready to move forward. Need a quick reminder?
Confidence Check
You've rebuilt the key ideas and practiced them with guidance. Now try these short questions on your own to check your understanding before moving on.
QUICK CHECK 1
Net-force calculation
Apply ΣF = ma with signs.
An 8.0 kg box has 28 N right and 12 N left. What is its horizontal acceleration?
Reveal Answers
2.0 m/s² right.
Why it works: F_net = 28 - 12 = 16 N, so a = 16/8.0 = 2.0 m/s² right.
QUICK CHECK 2
Elevator normal force
Use acceleration sign consistently.
A 70 kg person accelerates upward at 1.2 m/s² in an elevator. What normal force does the floor exert? Use g = 9.8 m/s².
Reveal Answers
770 N upward.
Why it works: With upward positive, N - mg = ma. Thus N = m(g+a) = 70(11.0) = 770 N.
QUICK CHECK 3
Static friction
Let static friction match the needed value below its maximum.
A 10 kg crate on a level floor has μₛ = 0.40. A 30 N horizontal push is applied and the crate remains at rest. What is the static-friction force? Use g = 9.8 m/s².
Reveal Answers
30 N opposite the push.
Why it works: The maximum static friction is μₛN = 0.40(98) = 39.2 N. Because only 30 N is needed for equilibrium, static friction is 30 N, not 39.2 N.
How did it go?
You've checked your understanding. Take one final look at the essential ideas before deciding what to do next. Need a quick reminder?
Summary
Before moving on, take one final look at the most important ideas from this review.
KEY TAKEAWAY 1
Diagram first, components second
A disciplined FBD plus declared axes determines the signs and equations.
KEY TAKEAWAY 2
Use the correct force model
Normal force, friction, and tension depend on the interaction and constraints; they are not universal constants.
KEY TAKEAWAY 3
Choose system boundaries strategically
Whole-system equations simplify acceleration; individual diagrams recover internal forces.
Ready for your next step?
You've reviewed the essential ideas one last time. Now choose the resource that best matches how confident you feel. Need a quick reminder?
Next Step
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