2C1 Mechanics Flashcards
Explore how mechanics encompasses the description of motion, Newton's laws, and the analysis of forces, energy, and momentum in diverse motion types.
Define:
Motion
The change in the position of an object over time.
It occurs when an object moves from one place to another and can be described in terms of displacement, velocity, and acceleration.
What is one-dimensional motion?
Motion along a straight line.
The object moves in only one direction, like a car driving down a straight road.
What is motion in two dimensions?
Motion in a plane (horizontal and vertical).
This kind of motion involves movement in both the x and y directions, such as a projectile launched into the air.
True or False:
In one-dimensional motion, an object can only move forwards or backwards.
True
One-dimensional motion is restricted to a single axis, meaning the object only moves in one direction.
Define:
scalar quantity
A quantity with only magnitude.
Scalars are described by a number (magnitude) only, without any directional component. Examples include mass, time, and temperature.
What are examples of scalar quantities?
- mass
- speed
- time
- distance
- energy
Define:
vector quantity
A quantity with magnitude and direction.
Vectors Scalars are described by a number (magnitude) and a direction.
What are examples of vector quantities?
- displacement
- velocity
- acceleration
- force
- momentum
What is speed?
Distance traveled per unit time.
Speed is a scalar and doesn’t account for direction, unlike velocity, which is a vector quantity.
What is the formula for calculating speed?
Distance / Time
It tells us how fast something moves, and is calculated by dividing total distance by total time.
A car travels 200 meters in 10 seconds. What is its speed?
20 m/s
Using Speed = Distance / Time, Speed = 200 meters / 10 seconds = 20 m/s.
True or False:
Speed is the same as velocity.
False
Speed is a scalar, while velocity is a vector (it has both magnitude and direction).
True or False:
Distance and displacement are both scalar quantities.
False
While distance is scalar, displacement includes direction and is therefore a vector quantity.
What is displacement?
Shortest distance from start to end, with direction.
It is a vector quantity because it considers both the distance and the direction of the straight line between the starting and ending points.
Define:
Velocity
The rate of change of displacement.
Unlike speed, velocity is a vector, meaning it also includes the direction of movement.
How is distance different from displacement?
- Distance is the total path length.
- Displacement is the straight-line distance.
Distance is scalar, while displacement accounts for direction and is a vector quantity.
True or False:
Displacement can be zero even if distance is not zero.
True
Walking in a circle results in a distance traveled but zero displacement since you end where you started.
Fill in the blank:
Energy is the capacity to do _____.
work
Energy is a scalar quantity and exists in various forms, such as kinetic, potential, thermal, and chemical energy.
Define:
Force
A push or pull that causes a change in motion.
It is a vector quantity and can change an object’s speed or direction.
What is the formula to calculate force?
Mass × Acceleration
This formula is derived from Newton’s Second Law of Motion, stating that the force on an object is the product of its mass and acceleration.
Fill in the blank:
The force required to accelerate a 5 kg object by 3 m/s² is ____ N.
15
Use the formula Force = Mass × Acceleration. In this case, Force = 5 kg × 3 m/s², resulting in 15 N.
What is momentum (p)?
The product of mass and velocity.
Momentum is a vector and represents how much motion an object has, given its mass and velocity. It is represented by p.
True or False:
Momentum is a scalar quantity.
False
Momentum includes both magnitude and direction, so it is a vector quantity.
Fill in the blank:
Acceleration occurs when there is a change in _________.
velocity
Acceleration is defined as any change in the object’s velocity, whether in speed or direction.
What is the formula for acceleration?
a = Δv / t
Acceleration measures how quickly an object’s velocity changes over time. It is calculated by dividing the change in velocity (Δv) by the time (t) taken for this change.
What does Newton’s First Law state?
An object will remain at rest or in uniform motion unless acted upon by an external force.
This law is also called the Law of Inertia. It emphasizes that objects resist changes in their state of motion unless a force causes a change.
Define:
Inertia
The tendency of an object to resist changes in its motion.
It is directly related to an object’s mass; the greater the mass, the greater the inertia.
What does the law of inertia explain about the motion of a car when you suddenly stop?
The passengers continue moving forward.
According to Newton’s First Law, the passengers’ bodies resist the change in motion and keep moving while the car stops.
True or False:
According to Newton’s First Law, an object can continue moving forever if no force acts on it.
True
In space, with no friction or other forces, an object would continue at a constant velocity indefinitely.
What does Newton’s Second Law describe?
The relationship between force, mass, and acceleration.
It states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (F = ma).
Fill in the blanks:
According to Newton’s Second Law, the acceleration of an object is _______ proportional to the net force and _______ proportional to its mass.
directly, inversely
This relationship means that for the same force, a larger mass results in less acceleration, while more force results in more acceleration.
True or False:
If you apply a constant force to two objects with different masses, the object with the greater mass will have greater acceleration.
False
According to Newton’s Second Law, the object with the greater mass will have less acceleration for the same force.
What happens when the force on an object is doubled?
The acceleration doubles, assuming mass is constant.
This follows from Newton’s Second Law: F = ma. When F increases, so does a, as long as m remains the same.
What is the net force acting on a 20 kg object with an acceleration of 2 m/s²?
40 N
Using F = ma, the net force is F = 20 kg × 2 m/s² = 40 N.
What is the acceleration of a 10 kg object when a force of 50 N is applied?
5 m/s²
Using F = ma, we rearrange to a = F/m. So, a = 50 N / 10 kg = 5 m/s².
What does Newton’s Third Law state?
For every action, there is an equal and opposite reaction.
This law explains that forces always come in pairs. If object A exerts a force on object B, object B exerts an equal force in the opposite direction on object A.
True or False:
According to Newton’s Third Law, the action and reaction forces act on the same object.
False
The action and reaction forces act on two different objects, but they are always equal and opposite.
How do action and reaction forces apply when a swimmer pushes against the wall of a pool?
The swimmer pushes on the wall, and the wall pushes the swimmer forward.
The force the swimmer exerts on the wall has an equal and opposite reaction, propelling the swimmer forward.
True or False:
Action and reaction forces cancel each other out.
False
Action and reaction forces act on different objects, so they do not cancel each other.
What is mass?
The amount of matter in an object.
Mass is a scalar and remains constant regardless of the object’s location (e.g., on Earth or in space).
What is weight?
The force exerted on an object due to gravity.
Unlike mass, weight can vary due to the object’s location. Weight is calculated using the formula: Weight = Mass × Acceleration due to gravity (W = mg).
What is the difference between weight and mass?
- Mass is the amount of matter.
- Weight is the force of gravity on an object.
Mass is constant and measured in kilograms (kg), while weight depends on the gravitational force acting on the object and is measured in newtons (N).
True or False:
Mass changes depending on the location of an object in the universe.
False
Mass is a scalar quantity that remains constant regardless of location, while weight changes depending on gravitational force.
Fill in the blanks:
Weight is a ______ quantity, while mass is a ______ quantity.
vector, scalar
Weight is a vector quantity because it has both magnitude and direction, whereas mass is a scalar and only has magnitude.
What units are used to measure mass and weight?
Mass is in kilograms (kg), weight in newtons (N).
The unit for weight (newtons) is derived from the formula W = mg, where g is acceleration due to gravity.
What is the gravitational constant (G)?
6.674 × 10⁻¹¹ N·m²/kg²
The gravitational constant is used in the equation for Newton’s Law of Universal Gravitation.
Fill in the blank:
According to Newton’s Law of Universal Gravitation, the gravitational force between two objects _______ as the distance between them increases.
decreases
The force is inversely proportional to the square of the distance between the centers of the two objects.
True or False:
The gravitational force between two objects increases if their masses decrease.
False
According to the law of universal gravitation, the force increases with mass, but decreases with the square of the distance between objects.
What is a gravitational field?
A region where gravity exerts an attractive force on objects.
The strength of a gravitational field depends on the mass of the object creating the field and the distance from it.
How does the Earth’s gravity field affect objects near its surface?
It pulls objects toward the center of the Earth, giving them weight.
This gravitational force is responsible for keeping objects, including people, anchored to the Earth’s surface.
True or False:
A gravity field is stronger the farther you are from the source mass.
False
The strength of the gravity field decreases as you move further from the source mass, following an inverse square law.
What is acceleration due to gravity on Earth?
9.8 m/s²
This is the constant acceleration that objects experience when falling freely near Earth’s surface, neglecting air resistance.
How is the force of gravity calculated on an object?
W = mg
Weight is the mass of the object multiplied by the local acceleration due to gravity.
True or False:
An object’s mass is always greater on the Moon than on Earth.
False
Mass is constant everywhere in the universe. What changes is the object’s weight due to the difference in gravity.
How does gravity affect objects in freefall?
Gravity accelerates all objects equally without air resistance.
This is why objects like a feather and a hammer, in a vacuum, fall at the same rate.
How does the mass of an object affect the gravitational force it exerts?
The greater the mass, the stronger the gravitational force it exerts.
According to Newton’s law of universal gravitation, the force increases as the mass increases.
What is the relationship between gravity and the orbits of planets?
Gravity keeps planets in their elliptical orbits around the Sun.
The Sun’s gravitational pull continuously pulls planets, preventing them from flying off into space.
How does the acceleration due to gravity change with altitude?
The farther from Earth’s surface, the weaker the gravitational pull and acceleration.
At high altitudes, g decreases slightly due to the increased distance from the Earth’s center.
True or False:
Gravity only affects objects on Earth.
False
Gravity is a universal force and affects all matter, both on Earth and throughout the universe.
What are contact forces?
Forces acting when two objects are in direct contact.
Examples include friction, normal force, tension, and applied force.
What is friction?
A force that opposes motion between surfaces.
It depends on the nature of the surfaces and the normal force.
True or False:
Friction always opposes motion.
True
Friction resists relative motion between two surfaces, no matter the direction of movement.
What is the normal force?
A force perpendicular to the surface of contact.
It acts to counterbalance the weight of an object resting on a surface, preventing it from accelerating through the surface.
Fill in the blank:
_______ is the force in a rope or string.
Tension
Tension is a pulling force transmitted through flexible objects like ropes or cables when they are stretched.
How does friction change with surface area?
Friction is mostly independent of surface area.
While surface area does play a role, friction is more strongly influenced by the nature of the surfaces and the normal force.
What is projectile motion?
Motion of an object under the influence of gravity and air resistance.
This motion combines horizontal constant velocity and vertical acceleration due to gravity, resulting in a parabolic trajectory.
True or False:
Horizontal and vertical motions are independent in projectile motion.
True
The horizontal motion is unaffected by gravity, while the vertical motion is influenced by gravitational acceleration.
What shape is the trajectory in projectile motion?
Parabolic
The combination of constant horizontal velocity and accelerated vertical motion results in a curved path.
What is uniform circular motion?
Motion in a circle at constant speed.
Although speed remains constant, the direction of motion changes continuously, meaning there is acceleration toward the center.
What is centripetal acceleration?
Acceleration directed toward the center of a circular path.
It is calculated as a = v² / r, where v is the speed and r is the radius of the circle.
True or False:
The speed is constant in uniform circular motion.
True
Speed does not change, but the direction of the velocity vector continuously alters as the object moves along the circular path.
What provides centripetal force?
Tension, gravity, or friction.
Centripetal force is the net inward force that keeps an object moving in a circle, and can be provided by different forces depending on the situation (e.g., tension in a rope or gravitational force in orbit).
Fill in the blank:
Centripetal force keeps an object in _______ motion.
circular
Without centripetal force, objects would move in straight lines due to inertia, as described by Newton’s First Law.
Define:
rotational motion
The motion of an object travelling in a circular path in a fixed orbit.
What is torque?
A force that causes rotational motion.
Torque (τ) is calculated as τ = rF sin(θ), where r is the lever arm, F is the force, and θ is the angle between the force and the lever arm.
How is torque related to angular acceleration?
Torque causes angular acceleration.
The relationship is given by τ = Iα, where I is the moment of inertia and α is the angular acceleration.
True or False:
Torque is maximum when force is applied perpendicular to the radius.
True
When force is applied at a 90° angle to the radius, it generates the maximum rotational effect.
What is the moment of inertia?
The resistance to rotational motion.
It depends on both the mass of an object and how that mass is distributed relative to the axis of rotation.
Fill in the blank:
The moment of inertia of a solid disk is ______ that of a ring.
less
The solid disk has mass closer to the center of rotation, making it easier to rotate compared to a ring with mass distributed farther out.
What is Hooke’s Law?
The force in a spring is proportional to its displacement.
It is expressed as F = -kx, where F is the restoring force, k is the spring constant, and x is the displacement from equilibrium.
True or False:
Hooke’s Law applies to all materials.
False
Hooke’s Law is valid only for materials that return to their original shape after deformation (elastic materials).
What is the period of a pendulum?
The time for one full swing.
The period is given by T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity.
What is work?
The transfer of energy through displacement.
Work is calculated as W = F × d × cos(θ), where F is the force, d is the displacement, and θ is the angle between them.
True or False:
Work is done when there is no displacement in the direction of the force.
False
Work requires a displacement in the direction of the applied force.
What is mechanical energy?
The sum of kinetic and potential energy.
Mechanical energy is conserved in an isolated system, meaning it remains constant if only conservative forces (like gravity) are acting.
Fill in the blank:
Mechanical advantage is the ratio of _______ force to input force.
output
Mechanical advantage quantifies how much a machine amplifies an effort force, making work easier.
What is the law of conservation of linear momentum?
Momentum of a closed system remains constant.
This law holds true when no external forces act on the system, such as during collisions.
How is momentum calculated?
p = mv
Momentum(p) is the product of an object’s mass (m) and its velocity (v). It represents the quantity of motion an object has, and the greater the mass or velocity, the greater the momentum.
True or False:
Linear momentum is a scalar quantity.
False
Momentum is a vector quantity, meaning it has both magnitude and direction.
Define:
Buoyancy
An upward force exerted by a fluid.
Buoyancy opposes an object’s weight, allowing it to float or sink depending on its density.
What determines if an object floats or sinks?
Its density compared to the fluid’s density.
An object will float if its density is less than the density of the fluid; otherwise, it will sink.
What is the formula for fluid pressure?
Pressure = force / area.
Pressure is exerted by fluids in all directions and increases with depth.
True or False:
Pressure increases with depth in a fluid.
True
The pressure increases with depth because the weight of the fluid above adds to the force exerted on an object.
What is fluid density?
Mass per unit volume of a fluid.
Fluid density is important in calculating buoyancy, pressure, and other fluid behaviors.
Fill in the blank:
Pressure in a fluid at rest is ______ in all directions.
equal
Pascal’s Law states that a change in pressure applied to an enclosed fluid is transmitted equally in all directions.
