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Flashcards · AP® Physics 1: Algebra-Based · Unit 2

Unit 2: Force and Translational Dynamics flashcards

57 cards on topics 2.1 to 2.9. Pick a topic or study the whole unit.

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2.1 Systems and Center of Mass

What is a system, and what makes an interaction internal or external?
A system is what you choose to study; the rest is the environment. Internal interactions are between parts inside the boundary; external ones cross it. Which is which depends on the boundary you draw.
How do you calculate the center of mass of a set of particles?
x_cm = Σmᵢxᵢ ÷ Σmᵢ, and separately y_cm = Σmᵢyᵢ ÷ Σmᵢ. Divide by the total mass, not the number of particles, and state the origin.
With the origin at a 4.0 kg mass, a 1.0 kg mass sits at x = 1.0 m. Where is the center of mass?
x_cm = (4.0 × 0 + 1.0 × 1.0) ÷ 5.0 = 0.20 m, nearer the heavier mass.
How can symmetry locate a center of mass?
The center of mass lies on every line of symmetry. A uniform symmetric part (plank, rod, plate) can be replaced by one particle of its mass at its geometric centre.
Must the center of mass be inside the object?
No. A ring's center of mass is at its empty centre.
When can a system be treated as a single object?
When its internal structure does not matter for the question: then model it as one object at its center of mass with the total mass. Not when the parts move relative to each other in a way that matters.

2.2 Forces and Free-Body Diagrams

What is a force?
An interaction: a push or pull on one object by another. It is a vector measured in newtons (N). An object cannot exert a net force on itself.
What are contact forces at the atomic scale?
Normal, friction, tension and applied forces are the large-scale result of electric forces between atoms at the touching surfaces. Long-range forces such as gravity need no contact.
What are the rules for drawing a free-body diagram?
One dot for the object or system; one straight labelled arrow per force exerted on it, starting on the dot. No components, velocity, acceleration or net-force arrows.
In which directions do the common forces act?
Gravity: straight down. Normal: perpendicular to the surface, away from it. Friction: along the surface, opposing sliding or the tendency to slide. Tension: along the string, pulling away from the object.
What are gravity's components on a ramp of angle θ?
Along the ramp (down-slope): mg sin θ. Into the surface: mg cos θ. Check with θ = 0: the down-slope part must vanish.
How many forces act on a thrown stone in flight, with air resistance negligible?
One: the gravitational force of Earth on the stone. There is no "force of motion" along the velocity.

2.3 Newton’s Third Law

What does Newton's third law say?
F_(A on B) = −F_(B on A). The two forces are equal in size, opposite in direction, the same type, simultaneous, and act on different objects.
Are the weight of a book and the normal force on it a third-law pair?
No. Both act on the same object. The partner of Earth's pull on the book is the book's pull on Earth; the partner of the table's push is the book's push on the table.
A small car and a heavy truck collide. Which exerts the larger force?
Neither: the forces are equal in size whatever the masses. The effects differ: the smaller mass has the larger acceleration.
Why can't internal forces change the motion of a system's center of mass?
Internal forces come in third-law pairs inside the system, so they sum to zero. Only external forces change the center of mass's motion.
Two people pull on opposite ends of a rope, each with 80 N. What is the tension?
80 N, not 160 N. For an ideal (massless, unstretched) string the tension is the same at all points.
Where is the tension greatest in a heavy rope hanging from a hook?
At the top, because that part holds up all the rope below it. A rope with mass can carry different tensions at different points.

2.4 Newton’s First Law

What does Newton's first law say?
If the net force on a system is zero, its velocity stays constant (same speed and direction). Conversely, constant velocity tells you ΣF = 0.
Does equilibrium mean the object is at rest?
No. Translational equilibrium means ΣF = 0, which includes moving at constant velocity, such as a lift rising at steady speed.
Is a ball at the top of its flight in equilibrium?
No. v = 0 for an instant, but ΣF = mg downward, so its velocity is still changing.
What is inertia?
The tendency of an object to keep its velocity. Objects slow down only because a force such as friction acts; no force is needed to keep moving.
What is an inertial frame in terms of the first law?
A frame in which the first law is observed to hold. An accelerating frame, such as a braking bus, is not inertial.
How do you solve a two-dimensional equilibrium problem?
Write one equation per axis: ΣF_x = 0 and ΣF_y = 0. Forces can balance along one axis but not the other; only the velocity component along the unbalanced direction changes.

2.5 Newton’s Second Law

What does Newton's second law say?
a = ΣF / m: the center-of-mass acceleration is proportional to the net external force and in the same direction. Apply it per axis: ΣF_x = m a_x, ΣF_y = m a_y.
How do factors of change follow from a = ΣF / m?
At fixed mass, a ∝ ΣF. At fixed net force, a ∝ 1/m: three times the mass gives one third of the acceleration.
What does the slope of an acceleration against net force graph tell you?
Slope = 1/m (in kg⁻¹), so the mass is the reciprocal of the slope. This is a standard way to measure a mass from data.
Should ma be drawn on a free-body diagram?
No. ma is not a force; it is what the net force equals. Only real forces exerted by other objects go on the diagram.
Is the tension in a string holding an accelerating hanging object equal to its weight?
No. Tension equals mg only when the hanging object has zero acceleration. Otherwise apply ΣF = ma to it.
How do you choose a system for a connected-objects problem?
Use the whole system to find the shared acceleration (internal tensions cancel). Then use a single part to find an internal force such as a tension.

2.6 Gravitational Force

What is the law of gravitation?
F_g = G m₁m₂ / r², with G = 6.67 × 10⁻¹¹ N·m²/kg² and r the centre-to-centre distance. The forces on the two masses are a third-law pair.
How do you find gravitational field strength at distance r from a mass M?
g = F_g / m = GM / r², in N/kg (equal to m/s²). Measure r from the centre, so add the planet's radius to any height.
The distance between two objects is tripled. How does the gravitational force change?
It becomes one ninth, because F_g ∝ 1/r². Halving r gives four times the force.
What is apparent weight, and how do you find it in an accelerating lift?
Apparent weight is the normal force (the scale reading). With +y up, F_N = m(g + a_y). It depends on acceleration, not velocity.
Why do astronauts in orbit feel weightless?
They are in free fall: gravity is the only force on them, so there is no normal force. Gravity is still large in orbit.
Why do all objects fall with the same acceleration?
Inertial mass (resistance to changes in motion) and gravitational mass (response to gravity) are equal by experiment, so mass cancels from a = F_g / m.
What is the equivalence principle?
In an accelerating frame you cannot tell the effect of the acceleration on apparent weight from real gravity.

2.7 Kinetic and Static Friction

What is the difference between static and kinetic friction?
Kinetic friction acts when surfaces slide: F_f,k = μ_k F_n. Static friction acts when they do not: it takes whatever value stops slipping, up to F_f,s,max = μ_s F_n.
A crate has F_n = 200 N and μ_s = 0.45. A 60 N push does not move it. What is the static friction?
60 N, opposite to the push. The maximum is 0.45 × 200 = 90 N, but static friction only matches what is needed. Do not write μ_s F_n for an object at rest.
How do you find μ_s with a tilting plane?
Raise the plane until the block just slips: μ_s = tan θ_slip. The mass cancels.
Which coefficient is usually bigger, μ_s or μ_k?
μ_s, for the same pair of surfaces. Both have no units and depend on the materials. In this model friction does not depend on contact area or sliding speed.
Does friction always oppose an object's velocity?
No. It opposes sliding or the tendency to slide between surfaces. Static friction on a walking person's foot points forwards.
What is the normal force on a block on a slope of angle θ?
F_n = mg cos θ, if no other forces act perpendicular to the slope. F_n = mg only on a level surface with no other vertical forces.

2.8 Spring Forces

What is Hooke's law?
F_s = −kΔx: an ideal spring's force is proportional to its change in length from relaxed length, and points back towards the relaxed position. k is in N/m.
How do you find a spring constant from data?
Plot |F_s| against |Δx|, draw one best-fit straight line, and take k as its slope using two points on the line (not data points).
A 0.30 kg mass hangs at rest and stretches a spring by 6.0 cm. What is k?
kΔx = mg, so k = 0.30 × 9.8 ÷ 0.060 = 49 N/m. Convert centimetres to metres first.
What is Δx in Hooke's law?
The change in length from the spring's relaxed length, not its total length. Subtract the relaxed length first.
Does the spring force depend on the object's direction of motion?
No. It depends only on position: a stretched spring pulls, a compressed spring pushes, always towards the relaxed position.
Does k change when a heavier load hangs on a spring?
No. The stretch changes; k is fixed for the spring, as long as it is not stretched beyond its proportional range.

2.9 Circular Motion

Why does an object moving at constant speed in a circle accelerate?
Its velocity is tangent to the circle and keeps changing direction. The acceleration towards the centre is a_c = v² / r.
What supplies the centripetal force?
It is not a new force. Real forces such as tension, friction, normal force or gravity, or their components, add up to ΣF_in = m v² / r. Never draw a separate F_c arrow.
How are speed, radius and period linked for uniform circular motion?
v = 2πr / T, so a_c = 4π²r / T². Period and frequency: T = 1/f.
What is the minimum speed at the top of a vertical loop?
v_min = √(g r). At that speed gravity alone supplies the inward force and the normal force is zero.
What happens when a string holding a whirled object breaks?
The object leaves along the tangent to the circle, not outward along the radius.
What is the net acceleration when an object's speed changes on a circular path?
a = √(a_c² + a_t²): the centripetal part changes direction, the tangential part changes speed.
What is the relation between period and radius for a circular orbit?
T² = (4π² / GM) r³, with r from the centre of the central mass M. Gravity alone supplies the inward force and the satellite's mass cancels.
How does doubling r affect a_c?
At the same speed, a_c = v²/r halves. At the same period, a_c = 4π²r/T² doubles.

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