A Topic Flashcards
Newton’s 2nd law of motion
F = ma: states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Newton’s 1st law
An object at rest remains at rest, or if in motion, remains in motion at a constant velocity unless acted upon by a net external force.
-inertia is the resistance to change in motion
- drag force and frictional force important to consider in real world
–if something is travelling at a constant velocity, the resultant force will be 0 as there is NO acceleration
Newton’s 3rd law
For every action, there is an equal and opposite reaction. This means that when one object exerts a force on a second object, the second object exerts an equal force in the opposite direction on the first object.
Circular motion formulas
Centripetal force (inward force = net) = mv2/r
Fsin(x) = mv2/r (horizontal): Conical pendulum (where the horizontal part of the tension in the string provides the force to keep the object moving in a horizontal circle). Swinging objects in a circle on a string, or “banked curves” where the horizontal component of the normal force provides the centripetal force.
Fcos(x) = mg (vertical): Conical pendulum (when the string makes an angle 𝜃 with the vertical).
Object in a circular motion on an incline or a sloped track.
used to analyze the forces acting on an object moving in a circular path when the object is suspended or supported by a string, rope, or cable — for example, in the case of a pendulum, a conical pendulum, or a rotating object on a vertical loop.
The force of gravity: components
F perpendicular = mg x cos(x)
F parallel = mg x sin(x)
General formulas
a = v/t distance = s(t) density = mass/volume
h = v2/2g
Normal force formula
- The component of the contact force acting perpendicular to the surface that counteracts the body
same as for F perpendicular: mg x cos(x) (inclined plane)
For horizontal surfaces (at rest) = mg
Fn =mg+F external (ifpushingdown)
𝐹n = 𝑚𝑔−𝐹 external (ifliftingup)
On top of the loop: Fn + mg = mv2/r
At the bottom of the loop: Fn - mg = mv2/r
Net force formula:
in one direction = Fa - Ff - Fg
in 2 dimensions = separate Fx and Fy components then use the Pythagorean theorem to calculate Fnet
using 2nd law = ma
Impulse-momentum correlation
J = change in p
– the area under a force-time graph is equal to the change of momentum
Projectile motion
vx = no horizontal acceleration, constant speed. vy = 9.81 m/s2 acceleration gradually increases speed
The horizontal velocity component gets smaller and smaller, while vertical component approaches a constant value in free fall (example from the plane)
Momentum (a vector quantity)
a measure of the motion of an object and is defined as the product of an object’s mass and its velocity, a vector
– linear momentum: p = mv remains constant unless the system is acted upon by a resultant external force
Impulse
the change in momentum of an object when a force is applied over a period of time
Force of tension
For an object hanging vertically at rest Ft = mg
For a hanging object: accelerating up Ft = mg + ma or accelerating down Ft = mg - ma
Object on a slope: Ft = mgsin(angle); no acceleration
Ft = mv2/r + mg (at the bottom; circular motion)
On a flat surface: pulling horizontally with friction: Ft = Ff + ma
The motion of bodies through space and time (a key in kinematics)
Position (s): describes the location of a body in a space relative to a chosen reference point. Measured in units of distance (e.g. m). Mathematically represented as an f of t s(t)
Displacement: change in position
Velocity (v): describes the rate of change of position with respect to time. It has both magnitude (speed) and direction, making it a vector quantity.
- Average velocity: change in s/change in t
Acceleration (a): Describes the rate of change of velocity with respect to time. Also a vector quantity, with direction indicating whether the body is speeding up or slowing down.
- Avg. acceleration: change in v/change in t
Relationships between them: data booklet equations
–> these equations crucial for analyzing straight line motion
Distance vs. displacement
Distance: a scalar quantity (only magnitude); the total path travelled by an object regardless of direction; always positive or 0
Displacement: a vector quantity (magnitude and direction); the shortest straight line distance between the initial and final positions of an object, including direction; can be +, - or 0
Instantaneous vs. average values for velocity
- Instantaneous velocity and speed are the measurements of how fast an object is traveling at any moment in time
- average velocity and speed are measurements of how fast an object has traveled over the whole journey (a good example is the car motion)
Uniform vs. non-uniform acceleration
- uniform acceleration is when an object’s accelerations stays constant
SUVAT equations only work for when an object is undergoing uniform acceleration - non uniform acceleration example: a runner running over hills
–> acceleration uniform in space (velocity can increase)
Projectile motion
the result of vertical and horizontal components of motion
- if we ignore the fluid (air) resistance we can assume that horizontal motion has a uniform acceleration of 0m/s/s
- we can also assume that the vertical motion of the projectile has a uniform acceleration of -9.81m/s/s
- if air resistance is present, there is a limited projectile motion
- horizontal motion is decreased leading to a shorter horizontal displacement
- vertical motion is reduced leading to less time in the air and a shorter max height
Terminal speed: occurs when an object stops accelerating downward and experiences a constant velocity
— the air resistance is great enough that it matches the F of gravity pointing down on the object
Forces (vector quantities)
describe the pushes or pulls that occur between objects and are central to the study of mechanics. A force is an interaction that can cause an object to accelerate, change direction, or deform. Measured in Newtons where 1N = 1 kg m s-2. Forces do not exist in isolation; they result from interactions between two or more bodies.
Frictional Force
- acts in a direction parallel to the plane of contact between a body and a surface
– different equations for a stationary and body in motion
- the force of friction must be equal and opposite to that of the pulling F
- the peak of the force and time graph shows the change from static to dynamic friction
- Area of the graph underneath is J (impulse)
- the greater the weight of an object, the greater the amount of friction
Field vs. contact Forces
Kinematics
the study of objects and their motion without consideration of forces
Spring
applies an elastic restoring F to each object attached to the spring
- Fh = -kx (k is a constant)
- the greater the stretch/compression the greater the restoring force
Hooke’s law
A stretched spring will exert elastic restoring force on either end of the spring and the amount of F produced is directly related to how much the spring is extended
