Unit 3: Forces

What is the primary focus of kinematics in physics?

Describing motion using quantities like position, displacement, velocity, and acceleration.

Which of the following best defines vector displacement?

The overall change in position of an object, possessing both magnitude and direction.

What does average velocity represent in kinematics?

The displacement divided by the total time interval over which motion occurred.

How is instantaneous acceleration mathematically defined?

The limit of average acceleration as the time interval approaches zero.

What condition must be met for kinematic equations of uniform acceleration to apply?

The acceleration of the object must remain constant in magnitude and direction.

What does the slope of a position-versus-time graph represent?

Velocity.

What does the area under a velocity-versus-time curve represent?

Displacement.

At the peak of its trajectory, what are the velocity and acceleration of a vertically thrown object?

Velocity is zero; acceleration is directed downward equal to g.

In two-dimensional projectile motion without air resistance, what happens to horizontal velocity?

It remains constant throughout the flight.

What release angle maximizes the horizontal range of a projectile over flat terrain?

45 degrees.

What is Newton's First Law of Motion also known as?

The Law of Inertia.

Which physical quantity serves as a quantitative measure of an object's inertia?

Mass.

According to Newton's Second Law, what is the relationship between net force, mass, and acceleration?

F_net = m · a.

Which of the following is true regarding action-reaction force pairs in Newton's Third Law?

They act on different objects with equal magnitude and opposite direction.

What is the condition for an object to be in dynamic equilibrium?

Net external force is zero while moving at constant velocity.

How does weight differ from mass?

Weight is gravitational force; mass is an intrinsic property measuring inertia.

What direction does a normal force always act relative to a contact surface?

Perpendicular to the surface.

What is static friction?

Resistive force opposing the initiation of sliding motion between surfaces.

How does maximum static friction compare to kinetic friction between the same surfaces?

Maximum static friction is generally greater than kinetic friction.

What parameters determine the force of kinetic friction acting on an object?

Coefficient of kinetic friction (μ_k) and normal force (F_N).

What is the component of gravitational force parallel to an inclined plane at angle θ?

m · g · sin(θ).

What is the expression for normal force on an object of mass m on an inclined plane at angle θ?

m · g · cos(θ).

What force provides centripetal acceleration for a car rounding an unbanked circular curve?

Static friction between the tires and the road surface.

What is the formula for centripetal acceleration of an object moving in a circle of radius r at speed v?

a_c = v² / r.

In an ideal string over a frictionless pulley, how does tension vary along the string?

Tension remains uniform throughout the entire length.

What force causes an elevator passenger to feel heavier when accelerating upward?

An increased normal force exerted by the elevator floor.

What is Hooke's Law formula for an ideal spring?

F = -k · x.

What does the spring constant k in Hooke's Law represent?

The stiffness of the spring.

Under what condition does Hooke's Law hold true for a deformable body?

Only within the elastic limit of the material.

What is Newton's Law of Universal Gravitation formula?

F = G · (m₁ · m₂) / r².

What happens to the gravitational force between two masses if the distance between them is doubled?

It decreases to one-fourth of its original value.

What is the SI unit of force?

Newton (N).

Which force prevents a block on a table from accelerating downward due to gravity?

Normal force.

What is a Free-Body Diagram (FBD) primarily used for in mechanics?

Isolating an object to show all external forces acting on it.

When an object moves at a constant speed in a circle, is it accelerating?

Yes, because the direction of its velocity vector is continuously changing.

What direction does net force point for an object undergoing uniform circular motion?

Directly toward the center of the circular path.

What is the work done by a force acting perpendicular to the direction of motion?

Zero.

What happens to kinetic energy when speed is doubled?

It increases by a factor of four.

Which law states total mechanical energy remains constant without non-conservative forces?

Law of Conservation of Energy.

What physical quantity is defined as the rate of doing work?

Power.

What is impulse mathematically defined as?

The integral of force over time, or average force times time interval (J = F · Δt).

What principle states that net impulse on an object equals its change in momentum?

Impulse-Momentum Theorem.

In which type of collision is kinetic energy conserved?

Elastic collision.

What characterizes a perfectly inelastic collision?

The colliding bodies stick together and move with a common final velocity.

What is the linear momentum formula for mass m and velocity v?

p = m · v.

What happens to the total momentum of a closed system during any collision?

It remains conserved.

What rotational quantity is analogous to linear mass (inertia)?

Moment of inertia (I).

What rotational quantity is analogous to linear force?

Torque (τ).

What is the formula for rotational torque produced by force F at distance r and angle θ?

τ = r · F · sin(θ).

What is the condition for complete mechanical equilibrium?

Both net external force and net external torque must equal zero.

What is angular acceleration defined as?

The rate of change of angular velocity over time.

What happens to angular velocity when a spinning ice skater pulls her arms inward?

It increases due to conservation of angular momentum as moment of inertia decreases.

What is the rotational equivalent of Newton's Second Law?

τ_net = I · α.

What motion occurs under a restoring force proportional to displacement?

Simple Harmonic Motion (SHM).

What does the period of a simple pendulum depend upon for small oscillations?

Length of pendulum (L) and acceleration of gravity (g).

What parameter does NOT affect the period of a simple pendulum in small oscillations?

Mass of the pendulum bob.

What is terminal velocity?

Maximum falling speed reached when drag force equals gravitational weight.

Which non-conservative force converts mechanical kinetic energy into thermal energy?

Friction.

What component of force produces displacement along an inclined plane?

The component parallel to the inclined surface.

How is gravitational acceleration g near Earth's surface derived from Universal Gravitation?

g = G · M_E / R_E².

What force keeps an object resting on a flat surface from falling through it?

Normal force.

What happens to tension in a string supporting mass m if the elevator accelerates downward at g?

Tension becomes zero (apparent weightlessness).

What term describes a frame where Newton's laws hold true without fictitious forces?

Inertial frame of reference.

What fictitious force appears in a rotating frame acting radially outward?

Centrifugal force.

In an Atwood machine with m₁ > m₂, which direction does the system accelerate?

m₁ accelerates downward, and m₂ accelerates upward.

What is the net acceleration of two masses m₁ and m₂ in an Atwood machine?

a = ((m₁ - m₂) / (m₁ + m₂)) · g.

What principle is primarily used to calculate resultant force in a system?

Vector addition of all individual forces.

In a pulley system with two weights, what parameter changes to balance the system?

Weight of the objects.

When a system accelerates, which force predominantly determines system direction?

Net external force acting on the system.

What happens to the restoring force in a spring if compressed instead of stretched?

It acts in the opposite direction to compression.

Why does a pendulum bob eventually come to rest despite swinging freely?

Due to air resistance and friction at the pivot point.

What is the effect of doubling object mass in a spring system under Hooke's law?

The resultant extension increases proportionally.

A block rests on a table; a second block hangs via rope and pulley. What force does NOT act on the hanging block?

Normal force.

Two objects are connected by a taut rope. Which quantities are identical for each?

Tension and acceleration.

A block hangs still in a vacuum. How many forces act on it?

2.

A block slides on a table connected to a hanging block via rope and pulley. What is true about kinetic friction?

It is less than the force of gravity on the hanging block.

A block rests on a smooth table attached to a hanging block via rope and pulley. What happens to the stationary block?

It moves.

A block rests on a flat surface with only gravity and normal force acting. Are these forces balanced?

Yes, the forces are balanced.

A car moves at constant speed on a level road under friction, drag, engine, and gravity. Are forces balanced?

Yes, the forces are balanced.

An elevator accelerates upwards. Are the cable tension and gravitational force balanced?

No, the forces are not balanced.